What are the relations between the level of power and abilities and the promotion of Pawn? In chess, pawn can promote to any other chess piece except King and get all the corresponding abilities and power. Similarly, in High School DxD, when Pawn promotes, their power level increases and they get other abilities also. For example, when Issei got a direct hit from Yubelluna's attack, he was protected by the Queen Protection abilities.

Let's take Issei's promotion to Queen (Akeno) as an example.

Are the abilities and the increase in power level the same for all the Pawns regardless of the power and abilities of the actual Queen (Akeno), or do they depend on that of the Queen?

And if Issei is King of his pieces and promotes himself to Queen, gaining abilities and power from both King and Queen pieces, will he be more powerful than Akeno?
No, the ability doesn't depend on the Queen of the group. I forgot whether it was Rias herself, or Azazel-sensei that said that the stronger Issei is, the longer he can stay in promotion as the promotion takes its toll on his body. If the promotion depends on the power of the team's Queen, then there won't be any need for Issei to improve his physical strength.

In the light novel, it was explained that each piece has a value. Queen worth 9 pawn, Rook worth 5, Bishop and Knight 2. So, rather than the strength of the Queen, the promotion increases the strength according to those numbers, I think. Of course the improvement depends on which piece he's going to promote into.

For example, Knight is worth 2 Pawns, so the ability improvement is more or less 2x of his ability as Pawn. However, it is not distributed evenly. Most of it will be distributed to the Speed. Queen, being all-round piece, will get an even increment to all abilities.