Undergraduate / Common App -Character Influence-Introduction-"ODD ONES" [2]

I think this has the potential to be a very interesting essay. I would deffinitely continue it.
Just be careful not to overdo it with too much fancy vocabulary. Other than that it's perfect.

Undergraduate / 'Progressive Equestrian Therapeutic Services' - UVA - favorite place to get lost [6]

If you really want to make the 250 limit there are a couple things you could take out.
"no pressure to be the person I strive to be" -- you could take this out and leave the bit about expectations, and it would still get your point across.

"the potential of the moment"
Also try to go back and re-word some of the sentences into shorter descriptions.

"I'm belting the lyrics to a World Gym sign." --That should be song.
"I could listen to rap without my mother's glares. Argue with myself and not worry about being right or wrong. Sing without worrying about pitch." --I think you can combine this and possible re-word it to make it shorter.

As for the second one, instead of "I learned to understand", I think it would sound better as: I finally understood...
In the last sentence the "they" is kind of vague.
I think the rest of it is really good.