A: Short answer: No.

Since Mystery Play requires you to play the exact card you draw from the top of the deck, there’s really no reason it should actually enter your hand at all. Having it go in your hand, even momentarily, opens up the possibility of it getting mixed with other cards you might prefer to play. Therefore, it should not be considered to increase your hand temporarily mid-resolution like this.

It’s draw and play the card you drew. Execute that in full, and then check your hand-size. It is most likely to still be the same size, unless the Mystery Play card you got increases your hand size for some reason (Draw Rule increase, Jackpot Action, etc.)