Can I take a skin tag off myself?

Yes. But if your instruments aren't sharp enough or clean enough you will regret it.
Depends. Depends on size of skin tag and the availability of clean instruments.
See below. Dermatologists usually don't recommend this, but if the stalk of the tag is very narrow, you could use a nail clipper or tighten a thread around the stalk. If you do this, you do run the risk of infection.