Is a miner running a full node? Is a miner just running a full node that is connected with the mining hardware? Or is there such thing as a miner node? Does it use additional software for transaction selection?

Thanks in advance!
Miners no longer run full nodes. They connect to a mining pool that gives them work to do. The pool runs a full node.

If you mine solo you'll need to run a full node but solo mining doesn't make any sense anymore because of variance. You can get a more regular income flow if you join a mining pool.