Shoes are always provided by Disney - you would never wear your own - so I wouldn't worry about this.
3. How hot does it get in Florida during the fall? My mom doesn't think I should even bother auditioning for performer because she thinks I'd die of heat in the heavy fur costumes. [I think it would be totally worth it

]
The hottest month is August in Florida - which averages high 90s. Disney takes great care of their characters and there are lots of ways to stay hydrated and safe during the heat.
4. If you go seasonal as a performer how long does that last? Is it sort of a forever thing, as long as you work at least one shift a year?
It would last forever, as long as you work the needed amount a year. It's typically more than just one shift, but it varies. You would also have to keep your color codes current by attending the special sessions they host. If your code gets over a year old, then you'll lose your status.
5. I understand that your Disney height and your physical height can differ, sometimes up to several inches. How does that play into being friends with fur characters? Couldn't you actually be physically too tall to be friends with someone even though Disney says you aren't?
While technically speaking this could be true - Disney doesn't really think about your real height at all, it's all based on what they measure you at. If one specific character looks off then you'll be disapproved in that character. If a lot of them look off you'll have to get remeasured.