1. You should be fine welding in the basement.

I would make sure you have a defined are , line the walls with
something fireproof and set up some movable screens to shield any other
basement storage items.

An air cleaner or simple exhaust fan may be advisable. Do a couple of
small tests, it should be very obvious if you generate enough fumes.
Any welding using a flux would certainly need an exhaust fan.


2. Check your covanants very carefully. In my area many have been found
to be unenforcable because they are too restrictive. You could always
build onto the house keeping the same style.