Checked with my department if my offer is conditional or not (remember, I am the one who got an conditional offer via e-mail and an uncoditional via post one week later).
It seems that my offer really is unconditional, except the fact that I finish my undergrad before october which will be no problem because my last exam is on 3rd July.
I didn't apply for funding but the department asked me if I would like to be funded. They first thought I'm from Ukraine because it's my birth place. As I answered that I'm a german citizen the department told me that I will be considered for full funding of tuition fees. This would be really cool though I'm not really depending on funding.