Actually... it ain't THAT different. Her hair is a composite hair of 'tiny Luna' and Nightmare Moon, done in a style similar to Celestia. Also, her voice is very similar to that of Nightmare Moon, again to point out that they WERE the same person.
As for why her appearance changed? At one point in the episode, she easily transforms (physically, not mentally) into Nightmare Moon again and back, which says to me that the rulers of Equestria are... well, let's just say they choose their appearance. 'Tiny Luna' is probably a shape she took more out of sheepishness than anything else, whilst this form is one taken out of a slow build-up of confidence over the course of a season. The rulers being able to change form certainly explains a lot (like how they're over 1000 years old but look relatively young).
Well, no. Not necessarily. I'm the youngest, I definitely don't act cute to gain favor. Mostly because my sister is nice (yet patronizing), and my twin/54 minute older brother (and he KNOWS it) preys on weakness. AND patronizes me. I tend to act nice, and that has not had any noticeable effect on how my siblings treat me. Certainly doesn't make them nicer. So again, I think she just used her inside voice because she was talking to family (who you speak informally with), and was small because she was weak at the moment.
When Nightmare Moon was defeated, her evil power was eradicated. Luna was reborn with her magic levels very low. It took time for her "good" power to come back to her, and now she's healed, reformed and rehabilitated and it's indicated by her magic mane.