Like someone said above, the academic job market in the humanities in Germany is very tight. You're somewhat lucky in your choice of location, as Hamburg is an academic hotspot of sorts and has 18 universities and colleges. A full list (in German) with links is
here. In addition to Universität Hamburg, Hochschule für bildende Künste, Akademie Mode & Design and maybe Hafen City University might be of interest for you, given your art and design experience. What is more, most universities and colleges have foreign language programs. I'd also look a bit further afield. Bremen, Flensburg, Kiel, Hannover, Lübeck, Magdeburg, Rostock, etc... all have universities and can be easily reached from Hamburg via train or car.
If you want to teach at a public school in Germany, you need a German teaching diploma and very very good German. However, there is a teacher shortage at the moment. Many states are actively looking for teachers and are also willing to consider qualified applicants without a German teaching diploma, though you'll have to take extra classes. The guidelines for public school teacher applicants without German teaching diploma in the city of Hamburg are
here. Again, I'd also consider the neighbouring states of Niedersachsen and Schleswig-Holstein. You'll have to look up their teacher application guidelines, since the conditions differ from state to state.
Private schools usually require a teaching diploma as well. You might have more luck at the various private language schools and institutes, which usually prefer native speakers and don't insist on formal teaching qualifications. Private Nachhilfeschulen, i.e. tutoring schools, are also looking for teachers and don't require a formal diploma. I'd also try Volkshochschule (VHS), a semi-public adult education organisation that offers everything from pottery and bellydancing to language classes. VHS operates on a contract per class basis and is a good way of tiding yourself over until you've found something else. The website of the Hamburg Volkshochschule is
here.
A lot of media and advertising companies are based in Hamburg and might be of interest given your art and design background. However, you would need very good German. I wouldn't bother with the museums and other public cultural institutions, since the Hamburg senate has just slashed the culture budget and many institutions are struggling or even closing.
If your German is good enough, I'd also look into freelance translating. You don't need a formal diploma (though it may be worthwhile to take the translator exam, if you want to make a full time job of it) and it can pay quite well, particularly if you find a niche.
Hope this helps and good luck!