I feel like there are others in the same boat as me, mllebamako and lucybelle, maybe?

I just had a conversation with my boss and I feel terrible now. I started working here in April part time (20h/week) and we kind of agreed that from June on I would change to full time. I don't know if they forgot about it and I didn't care so much. I don't need the money that badly and having free time is always nice, right?
Yesterday I asked if I could have three days off next week and today the office manager called and told me to go see boss lady. Which I did. Three days off is no problem and then she started going on about giving me more hours. 30h/week in August and then full time (40h) from September with a proper salary as well.
I'm a hopeless liar but I didn't actually have to say anything, so I felt super awkward but didn't say anything.

We're moving in September or October. I plan to quit at the end of August. If they hadn't offered me full time and a salary it would have been SO MUCH EASIER. I feel like such a flake now. And I also feel that I'm incredibly stupid for giving up on the offer of a full time position even before I've actually finished my degree to move to a new place where I don't even have a part time job so far, just to be with my boyfriend.
I'm debating when would be the best time to tell them that I want to quit? I have a super shitty contract right now, that does have the advantage that I don't have to give notice at all. But that's a shitty thing to do. I also don't want them to hate me or burn any bridges. (and I'd like to get a good reference...). I sort of suck at diplomacy when it comes to my own life. Ugh.

It probably wouldn't make sense for me to take on a full time position right now anyway, seeing as with the grant/scholarship I get I can't make more than 400€ a month. If I make more it gets taken off my free money. So unless they'd pay me considerably more than 400€+[scholarship/grant] and a proper contract, I which I'm pretty sure they won't because it'd amount to something close to 2k/month gross in order for me to make sense after taxes and health insurance.

I also got a letter from the scholarship/grant people saying that they want a lease or something from Germany. It's complicated, because it's a different place from the one I got money from when I studied in Poland (although it's essentially the same money). I wrote them that I don't in fact have a place in Germany right now and am planning to move back in September or October and for the time being still live in my rented flat in Poland. They told me that "if you're moving back in with your mother [...]" and I lost it right there. What the everlasting fuck? I've been living on my own for six years now. There's no way I can move back in with my mum (I never mentioned it, where the hell did they take that from anyway??) and I clearly stated that I was renting a place here.
They pay you less if you live with your parents and you're only entitled to the full amount if you prove you don't live with them. But WTF really?!