How to set gmail sync frequency? I want to know how often Gmail checks for new emails because I need longer battery life. How can I see/set this? I want to set it so that, for example, it checks for new mail every 10 minutes and never more often than that. 

I use this notification application on a Samsung GTi5800 that has Android 2.1update1
First, Gmail provides push email.. means, you get emails exactly when they arrive (if you are connected with internet).

Second, Gmail doesn't have dedicated sync module. It makes use of global Google Services Framework and Account sync module. You can turn off background data and Auto Sync from Accounts and Sync setting. When these are ON, sync is carried randomly.. but it runs when you connect to internet or turn these settings on.

To save battery, you can use toggle widgets (like Widgetsoid) to turn those settings on/off manually. Some provides way to force sync, too. To automate it, use Tasker app.

If your prime goal is to save battery, I would recommend you to use, Juice Defender. It takes care of all these effectively.