1) Hotmail - I have hotmail synching perfectly fine on my moto droid. Open the email app, click on manual setup, (may need to put in username first) click exchange account, (even if its not an exchange account) domain name is your full email address with nothing before or after it, put password in, put server as m.hotmail.com. I have not tried this on the incredible but it must be similar.
2) There are many task killer apps you could use but I would recommend not using one. The android system has a built in task killer that manages the running apps and services pretty well. Just let it do its thing.
3) Gallery app - In the app drawer there is an app called "gallery." This is your photos. You can press and hold on the app in the app drawer to put it on your home screen.
Hope this helps
I'm pretty sure you can uninstall Facebook, just not Facebook for HTC Sense. I could be wrong, though.
I'm not really sure how to keep it from being open. If you don't have an account logged in, I don't see how it would be using data and syncing... For now, I'd just go into Go into Settings> Accounts & Sync> Facebook for HTC Sense > Account Settings and set the update schedule to once a day, to be safe.
But, it really shouldn't be doing anything to drain your battery if you aren't using it. Froyo does a good job of keeping things on in the background but not letting it affect your battery unless it's using data or doing something... I'm pretty sure it just kind of lays dormant. The only way to completely get rid of Facebook is if you root your phone, sadly, there's a lot of bloatware on this phone when it's running stock.
Just don't obsess over it and Force Close it, that will just use more resources and battery because it will keep opening itself back up, and never get a task killer, Froyo doesn't need them .