In order to answer your question, pros and cons of the doubled pawns must be listed.
I shall start with pros:
- You get additional open file;
- You get additional diagonal;
- you get addition protective or attacking power;
Let me explain the last statement with the example from football. Imagine you have 2 players standing in a line, one being in front and the other behind ( just like doubled pawns ). If first player fails to stop the attacker, his "doubled" teammate ( the one standing behind ) can step in and stop the attacker. The same goes with offense -> if first player fails to score, the "doubled" teammate might step in, steal the ball and score. By doubling pawns, it is as if you play 2 versus 1, in the battle of controlling squares.
A small example can illustrate this:
[Title "White to move"]
[fen "k2r3r/pp3ppp/8/2p1p3/2P1P3/2P5/P4PPP/K2R3R w - - 0 1"]
White stands better here as he can play 1.Rd5!, thus obtaining the initiative, which gives him an advantage.
This is just an example, and the point is to consider what happens if Black is to move? If not for the doubled pawns, Black could follow the same plan ( 1...Rd4! ) and obtain advantage due to having initiative. That was the protective strength I talked about in the last statement above. It is as if you get double firepower on d-file and b-file.
The same applies in offense, and yet another "dumb" example can illustrate that:
[Title "White to move"]
[fen "7k/1pp5/8/2P5/P1P5/8/8/7K w - - 0 1"]
1.c6! b6 ( 1...bxc6 2.a5+- ) 2.c5! bxc5 3.a5 c4 4.a6 c3 5.a7 c2 6.a8=Q+ Kh7 7.Qa3+-
Again, you can see the supremacy White has on the b-file, because even if front pawn "misses" the mark, his "rear" friend will be able to strike.
I really hope that you understand now what I meant when saying that you get your firepower doubled.
To conclude: The strength of doubled pawns is the speeding up of piece development and stronger control of the adjacent squares.
Now is the time for cons:
- doubled pawn, the rear one, has limited mobility and is usually a choke point for his own pieces;
- rear pawn can't act as a normal pawn -> he can't support/protect the pawn he stood next to ( before he was doubled ) nor the pawn that stands in front of him -> he cant participate in controlling the square in front of the front pawn, nor the square in front of the pawn he "abandoned" by being doubled;
- by doubling pawns, additional "pawn island" is created which weakens pawn structure's defensive potential;
- in endgame, they can't create passed pawn since they are "held" by one opposing pawn;
Several examples must illustrate the above statements before I finally turn to the positions you mentioned in your post. Let us start from endgame disadvantage:
[Title "Doubled pawns are useless"]
[fen "7k/p7/8/P7/P7/8/8/7K w - - 0 1"]
As we can see, the above endgame is a draw. Doubled pawns can't enforce promotion to queen, because they act as single pawn.
As for static weaknesses of the doubled pawns, we can use the position similar to one from your post ( the Nimzo-Indian defense ):
[Title "White to move"]
[StartFlipped "0"]
[fen "8/ppk1bppp/8/2p1p3/P1P1P3/2P1B3/5PPP/6K1 w - - 0 1"]
Eventhough White is on the move above, the position is lost for him. Pawn at c3 is a choke point as he prevents bishop to defend the entry point for Black king. If this pawn was anywhere on the b-file, White would easily defend with Bd2, since piece coordination would not be hindered.
In the above diagrams, and in diagrams in your post, notice that side with doubled pawns have an extra "pawn island", and notice how this hinder pawn structure's flexibility.
As for their inability to act as normal pawns, this example might be good:
[Title "White to move"]
[fen "r4rk1/p4ppp/bp1n4/n1p1p3/q1P1P3/P1PBB3/3NQPPP/RR4K1 w - - 0 1"]
Although White is on the move, he can't defend c4 pawn. If c3 pawn was on b2 everything would be fine, since c4 pawn would have natural pawn support with b3. This example also demonstrates well doubled pawn being a choke point, because if c3 pawn was on b2 White could play Rc1, defending the pawn.
The best example demonstrating rear pawn's inability to act as a normal pawn is the following position:
[Title "Doubled pawn can't act as normal pawn"]
[fen "6k1/ppp2ppp/3p4/2nPp3/2P1P3/2P5/P1B2PPP/6K1 w - - 0 1"]
White can't dislodge the knight, yet if the rear doubled pawn was "normal" ( on b2 ) White plays b4 and kicks the pesky knight. Therefore, always strive to fore doubled pawns adjacent "neighbors" to advance. This will create the "hole" in front of the doubled pawns which is always useful outpost for your pieces, and that "hole" is permanent weakness.
Therefore comes logical conclusion for why doubled pawns are weak: They weaken pawn structure's defensive and attacking potential.
It is time to answer your questions, so let us start from the first position:
Why is this kind of double pawn particularly devastating for white?
[fen "4k3/ppp2ppp/3p4/4p3/4P3/2PP4/P1P2PPP/4K3 w KQkq - 0 1"]
This pawn structure is better for Black because he can defend his pawns with other pawns. White on the other hand has weakened pawn structure as he can't defend a2 and c2 pawns with nearby pawns. This means that Black can force White pieces to assume passive positions in order to defend the mentioned weak pawns, something like in my previous diagram.
Without the actual position with all the pieces, it is hard to analyze further so I will make necessary assumptions, in order to answer your question better.
First of all, d4 is very risky since Black plays ...c5! and puts your pawn structure under pressure.
If you exchange with dxe5 he plays ...dxe5 and will get slight pressure with ...Qa5. Your queenside pawns are scattered, and unable to defend, so you will go into passive defense ( I doubt you can use open d-file in such positions that fast to generate counterplay that will compensate a pawn loss ). Furthermore, he now gets excellent c4 square as a post for a bishop or a knight ( again, doubled pawn can't act as a normal pawn ). Black could also get slight pressure by playing ...Rfd8 or ...Rad8 at some point because your queen will have a hard time finding a good square ( ideal c2 square is occupied by the doubled pawn-> excellent example for doubled pawn being a choke point ).
If you exchange with dxc5 he could recapture with a piece and play ...Rc8 putting doubled pawns under pressure. Again, you will not be fast enough to generate counterplay against his pawn at d6 because you will waste time for the queen ( doubled pawn is a choke point again! ). The outpost on c4 would be even stronger then.
If you decide to "do nothing" Black plays ...cxd4 followed by ...exd4 and gets initiative because he will surely be better developed ( c2 pawn is a choke point ). He will trade d6 pawn for your e4 or c2 pawn and will have better chances in the endgame.
Therefore, you must keep your pawn structure flexible. Your best bet would be to maintain current pawn structure. Without seeing the rest of the pieces I can't give further advice.
As for the position in your 2nd diagram, the key is control of the e4 square. The ideas and features of that position are explained in any decent repertoire book so I will stop here because this post is too long already...
