Descriptions can be found here for all 16 types: link

She fits all of this.

I am pretty confident she is sensing over intuition and perceiving over judging but I'm torn between extravert and introvert as well as thinking or feeling. Would love to hear people's thoughts? :)

I am torn between ESTP, ISTP, ESFP & ISFP

she's more of an extrovert. She could clearly communicate about her feelings to Wardrobe, even though she's talking to her for first time. She could also confidently talk to LeFou and Gatson.
She's definitely a skilled negotiator as she could think of replacing her dad's place in prison quickly. So I;m choosing this. Though, ESFP is also quite close.

I agree with you about extravert, thank you for that. :)

I really think she's both feeling and thinking equally, which makes her so balanced, but her impulsivity is what ultimately makes me decide ESFP. Her decision to give herself in place of her father seemed to come from a more emotional place than logical place to me.

^i agree, she has both of F and T balanced in her.

She enjoys being alone by reading and feels difficult to get along with the town people. N because she follows her intuition and is a dreamy. F because she is kind and sympathetic. J because she is quite organized and not rushed.

anukriti2409 & hirohamada: Here are the parameters that I was going based on and would love to see your guys' so we can compare differences. :D

Extraversion vs Introversion:
Talkative/Outgoing (Extraversion) vs Reserved/Private (Introversion)
Prefer Fast-Paced Environment (Extraversion) vs Slower Pace Environment (Introversion)
Work out ideas with other/Think out loud (Extraversion) vs Think inside head (Introversion)
Enjoy being center of attention (Extraversion) vs Rather observe than be center of attention (Introversion)

Sensing vs Intuition:
Focus on reality of how things are (Sensing) vs Imagine possibilities of how things could be (Intuition)
Looks at concrete facts & details (Sensing) vs Looks at big picture, everything connects (Intuition)
Prefers ideas with practical applications (Sensing) vs Enjoy fantastical ideas for own sake (Intuition)
Describe things specific and literally (Sensing) vs Describe things figurative and poetic (Intuition)

Thinking vs Feeling:
Decide impersonally with logic (Thinking) vs Decide emotionally (selfish or selfless) (Feeling)
Value justice and fairness (Thinking) vs Value harmony and forgiveness (Feeling)
Enjoy finding flaws in argument (Thinking) vs Like to please and point out best in people (Feeling)
Described as reasonable & level-headed (Thinking) vs Described as warm & empathetic (Feeling)

Judging vs Perceiving:
Prefer to have matters settled (Judging) vs Prefer to leave options open (Perceiving)
Rules & deadlines should be respected (Judging) vs Rules & deadlines should be flexible (Perceiving)
Prefer detailed, step by step directions (Judging) vs Prefer to improvise along the way (Perceiving)
Make plans and like to be ready in advance (Judging) vs Spontaneous and welcome new surprises (Perceiving)

No INFP? Nope, just me?

^ I thought ISTP or ISFP could work but I don't think she falls under intuition over sensing/observing. I think she's very observant. :)