OF course it's possible. CPU mining isn't feasible now. All my GPU miners can do solo.
and which miner for amd video cards is better?
It should be phoenixcoin.conf without .txt
Put it in the data subdirectory.
NSGminer works well on AMD and supports solo. There are other miners which may deliver better hash rates, but they may or may not be able to do solo.
how to set up a miner? asks for a name and password, but there is no such thing in the wallet.