EEA parents with a british child

Hi everyone

I have a few questions. I and my partner are EU Citizens (Polish and Hungarian) living in the UK for 15 years and we have a child with British citizenship. Our claim for joined job seeker’s allowance has been discontinued after 6 months (I was the main claimer). My partner (who is also the mother) claims child tax credit, child benefits and housing benefits. My questions are:

1. Is she still eligible to carry on claiming the benefits although my claim for JSA has been cancelled?
2. Can she carry on claiming the benefits without being on JSA?
3. If she is not eligible, can she claim through derivative right to reside since the child is a British national?