Parallel Diagonal Pawn Structure -- a few questions.

I'd like to know about pawn structure in the diagram. The position is theoretical / unlikely / for illustration purposes only. 

1. Other than bishop mobility does this structure have much going for it?
2. ,How does the parallel structure play into the analysis?
3. Are there any opening(s) lines in which an approximation of this position may result. 

Here is version 1. 

Here is version 2. 

This is a little bit of a mess.  In d4 + e3 structures with the dark square bishop inside the pawn chain, c4 is usually played for.  A4 is certainly a common move in many d4 lines, often to restrain b5, but I'm not sure what it is doing here, and most especially what b3 has to do with anything.  

I think your effort to study this pawn structure without presenting a game you played is misguided.  With a game for context, we could help a lot more.  

I guess what I'm saying is there is no such field of study.  You could study D4/E3 structures with the dark square bishop inside the pawn structure, but whether A4 fits in who would be situational, and I can't right now think of a situation where b3 would also come into it.  You could also study pawn structure more generally -- there are many famous books, there is Pawn Structure Chess by Soltis, My System by Nimzowitsch and others.  

When it comes to Pawn structures and their effect on middle-game planning, my Bible is "Pawn Power in Chess" by Kmoch... although as noted by ArtNJ the book "Pawn Structure Chess" by Soltis is a decent (but somewhat watered-down) alternative.

When you talk about diagonal structures, are you referring to Pawn chains? The theory of Pawn chains is fairly well developed, and they've been under active study since at least the time of Nimzovich roughly one hundred years ago (cf: "My System" and "Chess Praxis", both by Nimzovich).

In general terms, by setting up a Pawn chain you trade away flexibility, mobility and balance for a rigid sturdiness on squares of a single color. The drawbacks of the weak color complex can be mitigated by maintaining a duo-Pawn adjacent to both the base-Pawn and the head-Pawn of the chain, and by retaining the opposite-colored Bishop to patrol the weak squares.

This sort of thing:

The Chain is f2-e3-d4, the head-duo is d4-c4, the base-duo is f2-g2 and the defending Bishop is at d3.

Kmoch - that is another good one on pawn structure. 

Of course, I probably should have started with this:  studying anything except tactics is a little bit premature given the 640 blitz rating and 500 something tactics rating.  

OMG, lichess tv was just showing a master game with the exact structure you were interested in!