Does donating cause anemia

No. All the red cells are returned to you. Basically, what they take out is fancy water. You will replenish your plasma is a very short period. Donate as often as they will let you.

I think I've given at least 70 pints of plasma.

If you are anemic already? But on meds for it, will they allow you to donate?

Normally no but you need to talk to the donation center.