I'm pretty new to iPhone. I was using Android for years and there was the problem that everbody could see if I've installed a app or not. How is this with the iPhone? Can anyone (for example friends on gamecenter) see what apps/games I've installed?
Your friends can see the games that have access to your Game Center account (this works accross multiple devices since you can have a single Game Center account for multiple devices).
The access to the game center needs an explicit autorisation. Most of the time on the first start of the game it will prompt you if you want grant access to the game center (or not).