When does child benefit/csa stop

Child has left full time education end of may,and claimed jsa------- will they be able to get jsa or only claim when mothers child benefit stops----which have been told is payable till September,
Also when will payment of csa cease for this child is that also when the child benefit stops in the September,or when child gets jsa-----
Child may also start part time work this week between 8-20 hours per week are the above benefits still payable if the child is working.

I know it's a muddled question and I appreciate any replies
Thankyou