Can I get tax credit for money donated to an inmate?

It's called a "gift". No credit available.

Ironically, if you gave this person gifts totalling more than $13,000, you would owe tax on the gifts, too.

Of course not! You don't get a "credit" for giving money to your baby sister or buying her a Christmas present, do you? Then why would you get one for giving something to a convicted felon??

As long as your gifts total less than $13,000 per year there are no tax consequences. If they are more than $13k, YOU must file a Gift Tax return and could even wind up paying gift taxes on your gifts.

no

donations are never deductible to a person only a qualified non profit organization recognized by IRS

and then only if you can itemize by using Sch A which would exceed your standard deduction

That is not a deductable donation. A deductable donation is one going to a non profit organization.

Aboslutely not. You are giving a gift to your friend.