Artificial trees are made of plastic which comes from oil. A live tree is grown for this purpose and when you cut one, another will be planted which will absorb the CO2 from disposing of the live tree. You have to use your artificial tree for more than 10 years in order to leave smaller carbon footprint than with using a live tree every year.
Unless it's pot grown and small, those trees rarely survive.
Exactly, it's no different than any other horticultural crop. Of course, if they removed natural forests areas to grow Christmas trees it would be different, but Xmas tree farms are usually made on agricultural land.