How can I figure out more about what my node is doing? if it verifies transactions sent from elsewhere, is it logged anywhere?
Since you are not running a full node, it only shares with the other nodes the blocks you are temporarily holding. Your node verifies transactions and blocks received from other nodes all the time.
I don't think that you can monitor it closer than the commands you mentioned.Edit: Actually, you might be interested in
this. I am not sure if you added 'debug=1' to your startup parameters.