I had my eye chalazion removed yesterday and I still have swollen under my eye lid which looks the same as a chalazion. Is this normal?

Yes, it is locally. draining, and follow your eye doctors advice on post-procedure healing efforts. Reduce computer usage over the weekend and baby the healing of your eyelid now for best recovery. The areas just incised will have some edema present from the inflammatory nature of your chalazion. It will improve daily.
Hard to say. Your best bet is to ask the doctor who completed the excision. You should understand that it's not uncommon to see inflammation and subsequent swelling and that may be what you're seeing presently.