>>33540170 (OP)
Who cares what other people think. You're not breaking any laws, so the important thing is that your relationship with this girl is positive and lasting. Your difficulties are going to be a) affording a single income household and b) making sure the cultural gap between you is bridged.
I don't know a lot about German economic conditions, but you are going to need to be making bank to have a housewife. Two cars is probably a necessity, and the whole point of a housewife is child care, so you are going to be supporting a growing family not just another adult. However, if you're spending all your time working, then a young, attractive woman is going to start getting bored. It's not going to be easy balancing work and your life together.
Another problem is that 13 years is quite a bit of a gap in cultural terms. She is not going to have any first hand knowledge of events or media that you consider formative, and the sort of things that she grew up with (tv shows, music, games, children's movies, etc.,) are going to to be foreign to you as well. You will each make references that the other won't get. A big one is that you are old enough to have grown up in a world where the internet wasn't ubiquitous, and she isn't.
The good news is that this gap can be mostly bridged, but it will mean spending a lot of time together talking, sharing experiences old and new, etc. You will probably have to watch a lot of media, read books, and listen to music you consider kinda cringey. Don't mock any of it. The bad news is that you'll also have to try to make friends with her friends, whom are probably not going to mesh so well with you. Trying to integrate friend groups is going to be rough.
Another problem is her parents. They are, understandably, not going to like the idea of their little girl being in a relationship with someone closer to their age than hers. My advice would be to be as respectful and deferential as you possibly can.