Yes, check the draft to make sure the Baro is set correctly.
yes, CO COULD leak from faulty gaskets, clogged chimney, low draft, etc....make sure you have working CO detectors.
As for running unattended, that will subside over time, it's like any other device, always worried about at first when your not used to it. As long there is no combustibles and your chimney is in good shape, shouldn't be any problems. I don't think I slept the first night with my new coal stove. LOL.
Most of us let them run 24/7. I usually lite mine in Nov and run it thru April.