I have a light fixture that I want to use in my living room. There is no power outlet in the ceiling so I was going to wire it to another cord to plug into an outlet. The light has three wires and the cord I want to use has only 2 wires. Can I do this?

The third wire in the light cord is a ground wire. That means that the light fixture is not double insulated. Get a grounded (3 wire ) extension cord.

No, you should not do that. And to be honest, what you describe, wiring a ceiling light into another cord to plug in, sounds like it may break code.

Help understand exactly what you are asking, please.

You have a ceiling light that you want installed, but there is no existing outlet in the ceiling, correct?

The correct way to do this is to have an outlet put in and pull the supply from either a nearby branch circuit already in the ceiling or extend the branch circuit that supplies the receptacle to an outlet installed for a new wall switch and then to a new outlet for the ceiling light.

The work itself is not that difficult, providing you have some knowledge of what you are doing. Also, this residence is your on home, call several "Licensed" electricians and request bids on the work. If you live in an apartment, then the work must go through you landlord.