Moving from Lone Parent to J. Allowance??

Hi I applied for lone parent payment like 12 weeks ago but inspector still hasnt come to see me although i have been gettin supplementary welfare allowance for about 3 weeks now. me and my boyfriend now want to move in together.

So will i get the full jobseekers allowance as he works and takes home 350 a week but will be goin to fas end of year as a 1st yr apprentice so he will be gettin like 230euro or something like that...

Will i still get my backdated money from lone parent payment if inspector hasnt seen me before i move out??

Can i apply for supplementary welfare allowance for JA, when i do move out as i think it takes weeks for it to come through??

Any info appreciated!