Is there any way to let Facebook run only when I want?
You could always install Titanium Backup (a GREAT app to have) or App Manager (was just released today by JRummy) and "Freeze"/"Unfreeze" the app when you want it to run or not run. This is a very quick/simple/painless operation and there's absolutely no chance for it to run (taking up resources or draining battery) while it's "Frozen" - it just takes up a bit of storage space is all.