Is it possible to sync apps and games from multiple PC's? I am trying to sync the apps from the same account btw!
Not necessarily. The dilemma is that if you have iTunes set to sync all apps - you better have all apps on all systems or you can end up deleting them when you sync (iTunes will prompt you before it does this.) If you have apps on your device, but they are not yet in iTunes, right-click on your device in iTunes and choose "Transfer Purchases" to copy those back to iTunes. Things to help: Set iTunes not to sync automatically, manage songs/videos manually, and sync selected apps. You can also trick iTunes into thinking the computers are the same: link
So I can authorize a new PC and transfer purchases and all my apps on my iPod will be copied to the new PC and no data of my iPod would be lost?
Yes. Even better would be to authorize the computer, then download all the apps first. Do a "transfer purchases" anyway just in case. Then when you backup on that computer you'll get your app data in the backup. I currently sync with two computers (home/work) and the only thing that has gone wrong was once when syncing at home it lost track of which apps I had set to sync, and went to sync all of them (was OK, I had to delete them though...)
For apps, yes. If you set music/videos to manual then it doesn't matter. If iTunes is not set to automatically sync, you can "transfer purchases" first.