Bildstein: I'll put my attempt in. For reference, I'm currently IGS 4k.
What is best play for each side?
From the diagrams, this looks like gote for both players.
If Black plays first, he captures three stones and surrounds three points of territory.
If White plays first, four of her stones get captured, she captures three stones, and surrounds two points of territory.
By my calculations, this makes the miai value (3 + 3 - 4 + 3 + 2) / 2 = 3.5
And I don't understand the concept of "count" well enough (or the differences with miai value) to answer the last question.
Bill: Congratulations, Bildstein! :-) This is a 3.5 point gote. As for the play, play could pause after or , but that is a minor point.
Now for the count. The question is how much the original position is worth? We call that the count rather than the score because it is not a final, scorable position.
What is the local score if Black plays first? Given that, and the fact that this is a 3.5 point gote, you can figure the count. You could also figure the count from the local score if White plays first instead of Black. Or you could figure the answer from the final results plus the fact that this is gote.