Notifications and Gmail sync?

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If you close the gmail app, you wouldn't get emails. It may be regarded as a core app though so you might find it starts itself up again. There is no need to close it though, it's fine just to leave it running in the background.

You used to be able to change the interval it checks for email, but you can't any more so I'm going to presume it's push. I've autosync turned off, I use K9 for emails etc and that's setup for push/IMAP. The default mail app on your handset may differ.

For FB, you should be able to control the frequency of that via the accounts & sync menu: (Settings -> Accounts & Sync).

Which handset do you own btw?

 

If it's push, it won't have much of an impact cos it's not constantly asking the server for mail.

If you've issues with battery life, turn off autosync and use the default mail app/K9 or similar. That was a massive help for me (that was before they updated the gmail app and removed the sync frequency settings though).

 

As far as I know gmail pushes notifications to your phone instantly.

I just set it up when I first got my SGS2 and as soon as new emails arrive on the server I get told straight away.

EDIT: Ah, Xyro beat me to it!