Okay, deep breath because it's just a phone and it can be fixed...even if it's by replacing it.
1. What kind of email are you trying to access via the email widget? If it's hotmail/gmail/yahoo/web-based, have you tried accessing it in the browser? Did you appear to have any issues while setting up account access the first time you used the email widget? (I'm also assuming you're talking about the email widget on the home screen and not an actual gmail "app").
2. (Not trying to sound like customer support)....but have you laid your phone down on a table that could have possibly been wet? I have seen/heard a report where some moisture/liquid apparently got inside the vents on the back of the phone and boo-booed the phone.
3. Keep in mind that any "app" that takes you to a website is just a redesigned shortcut/"skin" for that website. If you have a myspace "app" that doesn't seem to be working quite well, use the browser and load myspace from there. (Side rant: the Facebook app SUCKS, loading it via the browser forces the same view as the app, unless you hit the "full site" link at the bottom.)
4. If callers are getting a not-in-service message on your phone, that's an AT&T question. Sorry, no guesses on that one.
5. If you are on FB and want to save a pic to your phone, press a "long-touch" on the pic (like a profile pic)...it'll take you to their profile album. "Long-touch" one, and it'll come up in like a slideshow view on your phone. Long-touch it again, and it'll give you a save option.
6. Please elaborate on "change the format of my camera". What's the "little camera button" you're referencing? Are you talking about the camera app icon, or the actual camera button on the camera screen you have to push to take a picture?
7. Pics/music/movies etc to/from Captivate/computer: Info is here: http://www.samsungCaptivateforum.com/samsung-Captivate-how-to/usb-connection-failure-to-pc/