Do I mark whole yr for healthcare for child? Mom had coverage first part and me last, but I had child whole time.

Are you the child?  Are you filing taxes for the first time?  Did you have insurance for the entire year?

The child is my niece. Child was placed in my care first part of year. Child's mom had a medical card for the child. I had the coverage switched over from the mom's name to my name. I received form showing the months I provided coverage, but not when the mom had coverage. Do I mark just the months I show coverage or whole year?

Yes, if the child was covered the entire year you will select that she was covered all year even if it was not while she was living with you.