I am Swiss but I will attempt to answer this as good as possible:
1 Storage
#1 Storage YouYou get a bank account. Done. A bank account doesn't get you a lot of interest, but it is a safe way of storing the money and you'll have access to it at any time.
2 Bureaucracy
#2 Bureaucracy GermanyGermany is a little more bureaucratic than Switzerland but a simple bank transaction should be enough.
3 Taxes
#3 Taxes TheThe free sum "Freibetrag" which you can gift to your children is 400k EUR in Germany so you are good to go. This means no taxes for you or your dad.
4 Liability for parents in debt
#4 Liability for parents in debt IfIf your girlfriend doesn't accept the inheritance she's fine. You are not liable for the debt of your parents. If she would accept the inheritance she would also inherit the debt. So don't accept it and everything is fine.
Even if you were married and she accepted the heritage, it's still not your debt, but then your wife's. You can't be hold accountable for debt of your wife/husband, at least not in Germany.
5 Getting a flat with 10K EUR
#5 Getting a flat with 10K EUR NotNot gonna happen, at least not in Germany. You will need to save more and get a mortgage, but 10k is a nice start. You may want to start investing your saved money because you have the 10k security cushion on the bank account.
Edit: Free sum "Freibetrag" is actually 400k not 20k. 20k is for grandchildren I suppose, therefore the mess up.