If you back up your wallet on a usb stick and then restore it on another computer running the litecoin client, does the receive adress also come along. For instance, If some one would send money to an original address of the wallet, would it show up the new computer running the restored wallet?
A wallet is software used to access the block chain. It does not contain any coins. It just holds your keys. You can use the same keys on as many different computers as you want (just like you can make copies of your car's key and put them in any pocket you want), but you shouldn't because that might confuse you and result in lost coins.
Yes okay, but does the new client receive the new keys? So if I give out my address, then back up my wallet and load it on a new computer, does this new computer receive the keys when someone sends coins to the old address?