I kept using some faucets this week... I uninstalled BTC Core and Reinstalled it over and over, but always get the same message... Is there at least a pssibility to get my addresses back so i can use them with any other wallet?
Only if you have the wallet.dat.
If so you can
#1 use it on a friends machine (if possible) to export your private keys
#2 use pywallet to export the private keys yourself
#3 hire someone to do either #1 or #2
Option #3 comes with the risk that you are no longer the only person that knows the private key(s) for the addresses. It would thus be smart to hire someone to make a last final transaction that moves all your funds to an address from your new wallet.