Which side would you rather be in the three diagrams below?

Diagram 1: white, since he has the pair and can limit the c file.

Diagram 2: black, of course. Even though white has three minor pieces, the queen is far more superior and can quickly pick up pawns and pieces.

Diagram 3: black. 2 rooks is better than the lone queen here.

I agree with you on no. 1, but in no. 2 I think the three pieces work better than the queen, in no. 3 can't White trade the Queen for 2 rooks if they penetrate?

1. White, for the same reasons Chess4001 stated.

2. White, because white's pieces should coordinate against the queen and beat her. White's has no real structural problems so his pawns should be easily defensible.

3. Black, same as Chess4001

#3...pawns on both sides of the board, so queen is generally better.

I played some games from Diagram 3 with White and they really do illustrate and emphasise the ability of the Queen. While the Queen can often trade herself for two invading rooks the rooks can hardly do the same for the Queen; therefore I believe White has an edge in Number 3.

I'd play anyone that disagrees with me with those starting positions.

If I win, I've proven my point, if I lose, I've learned something about chess, so it's a win-win.

I don't think there's a convenient way to do it though. Can you create a challenge with your own starting position?

Principle: (heard this on a chess.com video!) the more pawns in a Q vs. 2R's game, the stronger the queen is! Also, in the starting position (8 pawns each on 2nd/7th rank), with one side having only a queen and the other only two rooks, the queen wins! So I'd say diagram #3 is the advantage is probably for the queen- the position has 7 pawns!

How should we get a game going? Using messages and the analysis board?

Ok, I took a look at number again and decided to change my mind. White has the pair and doesn't have much exploitable weaknesses.

I tend to believe that white should be better in each of these positions. Mostly this is just quick intuitive assesment but to mention few possible reasons each position is relatively closed which should probably favour the type of material white has and white has the advantage of the first move which can be quite telling as black isn't ideally coordinated.

By the way, is there some deeper meaning behind having the white pawn in a3 in the first diagram but in a2 in others?

No, the position of the a-pawn shouldn't make much of a difference.