As an artist : Yes, her best songs are self written yet sadly unknown.
As a person : I can't really say since I don't know her personally, none of the people or fans here do. I respect what she does as an activist for mental health. She inspired a friend of mine to come clean to her parents about her addiction and now she's 2 years clean. My friend is probably not the only one she inspired, there's probably hundered more, and if that doesn't gain her my respect I don't know what does
Hell no. What the hell for? I respect actual groundbreaking astounding women. Not some rude celebrity that got famous as a cute teen. (And nope, I don't respect Ariana either. )
I think she's a really talented singer but I don't respect her as an artists because she's just so desperate to be big. I remember this interview of her saying she didn't understand why she wasn't #1 if she was talented and then realized she needed hits an all that stuff.