If you're getting texts without any issues, the FB SMS issue is probably on the Facebook end. I have mine linked to my gmail account so that I get notifications immediately. For your emails (assuming you are using the email app), make sure you have it set up to retrieve emails automatically. From the inbox of each account you have set up, press menu>settings>... crap, I don't know where to go from there because I'm not currently using that app and I can't check the settings without having an account setup, but it's in the settings somewhere. Basically, you can set how often the app checks your email server to see if you have any new mail. If your issue is with the gmail app, make sure you have sync enabled, from your homescreen, press menu>settings>accounts & sync, choose your gmail account and make sure gmail is checked. If all this stuff checks out and it still isn't working AND you have a task killer set to automatically end tasks, you may be inadvertently killing something that these things rely on.
