Question

how is oxygen used for cutting and welding purposes

Answer 1

Oxygen is used as a fuel for cutting and welding. It is used with acetylene and commonly called as Oxy-fuel welding and cutting.
Oxy-fuel welding:
Metals are welded using welding torch. The metals needed to be welded are heated to a temperature so that they can reach molten state, then additional metal is introduced between the two molten metals called filler.

Oxy-fuel cutting:
Again in this metal is heated to a particular temperature and then stream of oxygen is passed which turns the metal into metal oxide and cuts from that part.