Even when Madoka does form an opinion of her own, she is not always confident in it. She tries to get Sayaka to consider befriending Kyoko, but when Sayaka shoots that down Madoka just shuts up and starts rethinking things all over again. Madoka constantly looks for compromise and does not want to have a conflict with anyone, and is weak-willed enough to sometimes bend her opinion to avoid trouble.Madoka the magical girl is also shown to compromise in social situations: she may be absolutely confident in battle, but she was still staying neutral between Sayaka and Homura.

This is because Madoka is an observant person, who typically ends up watching rather than acting. That much should be plain and obvious, as observing is her entire role in the show. Though she may seen like a clueless ditz based on all of the clueless faces she makes, Madoka is the type of girl to think things through. She is slow and uncertain with her decision making, and as a result, rarely commits to a decision. This has already been hinted at, because Madoka does not pick sides in a conflict, but just thinks both sides through and never says who she supports. She tends to sit on the fence throughout the whole show, her biggest decisions being to run away.
Madoka doesn't observe and decide alone either. When she's trying to decide something, Madoka will not hesitate to talk to people about it. She is generally in control of her thoughts and emotions, or at least trying to be. When Mami dies, Madoka avoids a major emotional break down until she is about to talk it through with Sayaka. Until she has a chance to deal with them properly, she makes an effort to put a lid on her feelings and act normally. This Madoka has largely gotten over her habit of running away, but that does not mean that she won't think things through very deeply and sometimes struggle with her choices. But she no longer struggles as much with being confident, but with wanting to make the absolute best decision.

The decisions Madoka makes without talking to people are driven by strong emotions, generally fear. She stops the group suicide impulsively because she doesn't want to die, she throws away Sayaka's Soul Gem on impulse to stop Sayaka from fighting, and she shoots Mami because she's scared of seeing someone else die. It's only after Madoka commits these acts that she realizes what she's done and she usually crumbles under the pressure and confusion following her decisions, while seeming confident until they are completed. It might also be noted that her impulsive decisions were all made in an effort to protect someone; Madoka will think for eons about herself, but will act quickly to prevent someone else from getting hurt.

In all of the timelines Homura experiences, Madoka has died because she wanted to protect people as a Puella Magi. In one timeline, she even asks Homura to destroy her Soul Gem, essentially destroying Madoka's soul, rather than allow her to become a witch and hurt people. Even when Madoka is laying there dying, she is thinking about the fact that she wants to protect people. When Madoka makes her miraculous wish, it makes it impossible for her to exist and sets her in line to absorb suffering for the rest of eternity, but Madoka is completely content as long as she is helping people. Kindness and loving everyone is a huge part of her character.

When she's a Puella Magi, Madoka feels that she is worth something. And when Madoka feels like she's worth the life she's been given, she confidently works to protect it. There is a dramatic difference between the Madoka who prevents the suicide, scared out of her wits and lacking confidence in her ability to save those people, and the Madoka Magica who protects Homura in the first timeline. There's a huge difference in the Madoka who falls to her knees and breaks down when Mami dies in the line of duty, and is consumed by the terror of the witch Charlotte, and the Madoka Magica who looks down at Mami's corpse and Homura before she confidently heads off to fight the killer witch, all in the name of saving those precious to her. Even something as simple as her day-to-day interactions with people can be changed by a boost in confidence; when she is a Puella Magi, Madoka approaches Homura and leads the way to the nurse's office, while talking confidently and cheerfully with her. In another timeline, when she is not a Puella Magi, Madoka follows Homura and performs the same conversation, except this time she is stuttering and unsure. Her shy and timid nature will give way to a more happy ad upbeat girl when she feels good about herself.
In the end, unless Madoka feels confident in herself, she cannot and usually will not act useful, because she's too caught up in the fact that she doesn't think that she can be useful.

Lastly, and possibly most importantly, Madoka is a very pure girl and she is full of hope. It starts in her character design, where Madoka is noted for wearing pure and innocent white stockings, and ends in her purpose in the show. In Puella Magi, the transition from hope to despair gives off energy. And Madoka has the potential to be the strongest Puella Magi with the most hope, and therefore she can become the strongest Witch. This can be seen as the fact that Madoka is able to soak up a lot of despair before her heart breaks from the sadness. Even after all of the terrible things that happen in the show, Madoka still has hope that something good can happen. She believes that she can save Mami from her loneliness, that Homura can work with Sayaka and it'll turn out okay, and even once Sayaka is good and dead, Madoka believes with Kyoko that they can save her soul. Even after Kyoko, Sayaka, and Mami are all dead and Madoka Magica is crying her eyes out, she pulls herself together to fight Walpurgis Night with Homura.

Madoka might cry and break down a lot, but despite all of the tears she sheds, she is a strong girl who does not give up and wants to keep protecting people. She continues to look towards the future throughout the entire series. And when she finally makes her wish, it is to protect the Puella Magi who make a huge sacrifice for their own hope and wishes. Madoka essentially becomes Hope when she makes her wish, which is quite the indication of just how much Hope is in this girl's character.

The "real" Madoka made such a huge wish that she broke the barrier of time and space. Her enormous wish and equal magical power brought Madoka from a human existence to one practically on par with a god. Her past self had defeated the most powerful witch in the world with one shot, and this Madoka had more power than that girl. Her wish allowed Madoka to appear to every magical girl in any world or time right as she was about to evolve into a "witch", and destroy her soul gem before it became a grief seed.

This Madoka, however, is only a copy of that Madoka. In Mayfield, all characters start with none of their special abilities or powers. They have to regain them from the post office. Madoka has only regained a portion of her "real" belongings, which means that she only has a fraction of her "real" God-like abilities.

Madoka's regained abilities include...

→ Her Soul Gem: The most important aspect of a Puella Magi is probably their soul gem. It is literally her soul given a physical form. At this canon point, it is also shown to be giant---- so big that it is chilling in outer space and seen about to collide with Earth. Luckily, Madoka's soul gem has also been shown to be scaled down; even in official Ultimate Madoka artwork, she has her soulgem necklace drawn, which supports the idea that she should be able to scale it down. So for RP sake, her soul gem will always be able to fit in her palm.

It has three forms. The first is as an egg-like gem, the second as a small ring, and the third as a decorative gem on her transformation outfit. Her soul gem remotely controls her body, which does not have a soul in it. For this reason, if she is separated from her soul gem then her body will stop moving and resume being a corpse. Her body can also continue moving as long as her soul gem is in tact.
This may seem inconvenient, but it is actually very helpful. Because of the separation of her mind and body, Madoka does not feel pain as strongly as a normal human girl. Her body could be stabbed and she would only feel a fraction of the pain. The general rule is that she cannot feel enough pain to render herself unable to fight. Her body can still give out if it cannot physically function, but Kyuubey suggests her magic would be able to eventually heal that.

Finally, for a normal Puella Magi there would be a danger of their soul gem tainting. This happens if they go too long without purifying it with a "Grief Seed" (or other purification methods). It can also taint if they fall into despair and begin cursing the world around them. If this happens, Madoka will become a witch. Her witch form is Kriemhild Gretchen and is kinda really bad news. She can end the world in less than 10 days at her canon point. Luckily! Madoka has~~~

→ Soul Gem Purification Powers: This is a product of Madoka's wish. In canon, Madoka is able to teleport to any Puella Magi who is about to turn into a witch and purify their soul gem. However, this is because she shot time traveling Magical Madoka arrows in her canon. Those arrows have not been shot in Haven and weren't shot in Mayfield either, so the teleporting will not apply. Instead, Madoka will have to physically reach a Puella Magi and purify their soul gem by hand. This means that she will not have a 100% success rate, giving any Puella Magi characters in Haven the option of becoming a witch. I'll set up a permission's list. When she purifies a soul gem, it also disappears... so it would be a mercy kill.

In the case of Madoka's soul gem, if it is about to hatch into a witch then a second Madoka would appear and destroy the first. The only time she can do this is to prevent herself from becoming a witch. It might be noted that in canon, Kriemhild Gretchen had actually physically hatched before she was destroyed. There may be a short lag period where Gretchen attacks people before a new Madoka destroys her.

→ Her Magical Girl transformation: She actually has two. Madoka's Ultimate form is never fully explained in canon, but she is seen to be able to transform to her "usual" Puella Magi self and then to Godoka. In RP, Madoka will only pull out her Ultimate form if she feels it's appropriate. Otherwise, she'll prefer transforming into her first form. There isn't really a power difference between them. Just outfits and hair.

→ Magical Powers: Madoka fights with a rose-themed bow by firing magical pink arrows. The drama CDs imply that Madoka can also do other things with her magic (she makes Homura run fast in PE) but since that's never fully explained in canon I will not be using her magic for anything but fighting with arrows. Madoka is super powerful, but I will be watering down her powers for the sake of roleplay. When she uses magic, Madoka's soul gem gets a small taint.

→ Soul Gem
→ Rose Bow
→ School Uniform

Water was an essential part of any life. Whether it was in Mitakihara Town or Mayfield, Madoka knew that water was important. So it was the same in Haven and worth the risk. Madoka carried a bucket in one hand and her rose bow in the other, fully transformed and cautious as she made her way to the well.

She knew her new room mates would have happily done this themselves, but felt it was more appropriate for her. Her soul was encased in its soul gem and her magic would help her to protect herself. If something happened then she would be least likely to be bothered by it. That, and she knew she wouldn't be able to bear waiting for her room mates to return. She'd have worried and eventually gone after them.

Madoka looked down the well and set the bucket in place, taking a deep breath before proceeding to draw out some water. Even now, with her unable to protect them if something happened, Madoka was worried. "I need to get the water back quickly... please be okay, everyone."