What can you do to promote a better tone, a better embouchure, and better intonation on the piccolo?

I own a flute, and I recently was forced into playing piccolo. The piccolo I was given is a YPC-32 piccolo, and it really isn't the best piccolo you can use to play. I am struggling with playing piccolo because I really am not used to playing an instrument like the piccolo. When I play piccolo, I tend to have a very tight embouchure, and that promotes an airy, shrill tone. I have trouble reaching the upper register, and I find it really difficult to have the right air velocity to play notes on the piccolo. What main things can I do to reach the upper register easier, have a warm tone, and keeping intonation, because that is something that really bites me when it comes to playing the piccolo. Thank you. :)