My favorite Non Disney Princess Song is I Want My Tears Back by Nightwish and I think that song would suit Snow White, but not perfectly because she's not very imaginative, well not that much compared to some of the other princesses

Just so that you know with Favorite Non Disney Princess Song I'm talking about any song, not just from various movies, but also outside of the movie world and the song can be from other Disney Movies too

Oh I thought you meant song from a Disney movie without a Princess...in which case is "Baby of Mine" from Dumbo.
It's hard for me to choose a favorite song...I have so many, but one of my all time favorites is "I Wanna Dance With Somebody" by Whitney Houston, which would totally fit Cinderella.

Far longer than forever wouldn't suit Ariel nor would Let me be your wings but I think soon would

My favorite song is When You Wish Upon A Star, I think that would suit Ariel well.

I love the icons! I like so many songs!

What the Water Gave Me by Florence + the Machine.
And oh, poor Atlas
The world’s a beast of a burden
You’ve been holding on a long time
And all this longing
And the ships are left to rust
That’s what the water gave us
I think that could fit Mulan because she feels like she has this burden of her secret, as well as the times when she feels "all this longing" when she's around Shang, but since she has to pretend to be a man, she can't let on.

‘Cause they took your loved ones
But returned them in exchange for you
But would you have it any other way?
Would you have it any other way?
You couldn't have it any other way
This would be like how they came to draft her father, but then Mulan came up with her plan and "returned them in exchange for you." Also, how she doesn't really want to do it, but she wouldn't/ couldn't "have it any other way."

‘Cause she’s a cruel mistress
And a bargain must be made
But oh, my love, don’t forget me
I let the water take me
Again, the first part would refer to her father and how she took his place because "a bargain must be made." I also think this part could refer to when Shang left her on the mountain. The "bargain' would refer to how he didn't kill her because she saved him first. The "cruel mistress" could refer to the law. Letting "the water take me" could refer to if she were to go home, but that part could also sort of refer to when she went to the imperial city and how, at first, Shang didn't believe her.

Now I'm remembering Why Don't you Do Right- I guess that could in a way.

Chasing Cars for Ariel? I don't know...maybe Fireflies can fit though.