if u got regional preferences make sure the IP matches your preference, otherwise go to WBC and change regional settings...
Changing host will have no affect as long as your site do not stay off line for many hours. Try to move the hosting in quick time without any or much down time.
I honestly do not think so. Simply upload your site to the new server and change the DNS. Once the DNS updates just wait a few days and delete the old one. No one will ever know the site was changed at all.
Leave the old site up on the old IP for about 48 to 72 hours. It takes about that long for all the routers on the internet that have your IP / DNS cached to get the new IP address. That way you won't have any interruption problems. As long as your domain and URLs stay the same your rankings won't suffer. I had to move servers 3 times my first year to keep up with the load and didn't have any trouble.
It should not make any difference just make sure you give the dns time to update so it doesn't mess up the indexing
Others reported some harm on changing hosting and it really hurt their traffic and rankings. Make sure you will get a better one, check the reviews, avoid shared hosting.