1 year contract position verbally accepted from company A and just got a call from company B to move to final interview stages

So, I suppose I'm counting the chickens before they hatch, but a bit of a back story so I interviewed for both places around the same time (3/18 - A and 3/29 - B).

First one was a 1 year contract that needed to be filled ASAP, so I heard back from them literally at the end of the next week (3/29) that they would like to move forward with hiring me. I accepted, and they gave me a start date of 4/15.

Also, I know I probably should've waited to hear back after Company B's interview, but I got really excited about company A. And also, I didn't think I did that hot in the interview with company B.

Well, I just heard back from company B, and they want to move forward with the final interview tomorrow (they originally wanted to interview me on 4/16, but I said I only had this week available). And in the case that I do get the position. I have a feeling they'll notify me 2 to 3 weeks into the position that I just accepted with company A.

So I guess my questions are:

Should I tell company B in tomorrow's interview that I accepted company A's offer or that I have an offer so that they can tell me sooner than later?

If I do receive the position at B, how would you go about telling company A, after having worked there for a couple of weeks?

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