Question about claiming dependents w/Medicaid

My daughter and grandchild live with me and my significant other and have for the entirety of 2020 (and will in 2021). My daughter and grandchild are both on Medicaid and receive EBT benefits. There is no actual income involved for my daughter for 2020. 

We're trying to figure out who can and should claim them, and if doing so impacts their Medicaid coverage going into 2021. 

Do you know:

1. In order for them both to be covered by Medicaid going forward, my adult child has to file a return and claim her child, even if she had no income?

2. If there is no requirement for her to claim her child in order to stay on Medicaid, I know I would be able to claim them both. Right? 

3. But can my SO claim them? We are not married, have been living together for 15 years and jointly own the home. It may benefit his tax burden more if he is able to be the one who claims them but we just don't know the best way to proceed. 

Thanks for any guidance!