".I dont even know if it transfered the apps to my iTunes. What should I do? "
Look and see if it did.
"Also, is iOS 5.0.1 the latest version? "
"How do I check if my Facebook and my Twitter is up to date??"
look to see if there is an update availble for them.
"everytime I sync my iPhone to iTunes it keeps syncing notes and mail account even though it did that the last min I synced my phone in..is it still OK?"