Hello all. Here are some general questions I have come up with. Please provide any feedback you can. Much appreciated!

1. If you have the option of placing either Rook on an open file, which one do you move? Does it depend on the function each Rook is playing?

2. With regards to calculation, what are the comparison and elimination methods?

3. How many squares constitute a diagonal? Is a5-d8 just as much a diagonal as a1-h8?

4. If a square is guarded by a piece, but not a pawn, is it still considered "weak"? Or would you say that the square has the potential to become weak?

5. What is a "solid" position? Is it one in which all pieces and pawns are defended, or is it a position where your opponent has trouble finding a way in?

Thank you again.

1.
When this is a difficult question it's either because it's currently unknown which files will become open, or there are more than 2 files open/subject to being opened.

For example in the queen pawn games (1.d4 d5) there are often exchanges that open the c and d files.  So the queen rook to the c file and king's to the d file.  If white has dreams of playing e4 and opening the e file (sometimes the case) then the king's rook goes to the e-file and the queen's rook must chose which is more important the c or d file.

The other decision point is tactical.  After 0-0 if you take the open e file with your king's rook as part of a tactic or attack, it's possible RxR+ can be an annoying intermezzo disrupting your tactic.  So in that case you'd play the queen's rook over.

2.
Calculation is guided largely by experience i.e. the patterns you have in long term memory.  There are a lot of factors that go into choosing some moves while discarding others, many of them not easily expressed in words, and I'm sure no small number done unconsciously every game.  Sometimes it's called a chess player's intuition.  A general method is that you want your moves to be as multi-purpose as possible and keep your pieces as mobile as possible.  If a queen can defend from 3 different squares, is there one where it's attacking something else or defending a weakness?  Does it get in the way of any of your pieces?  Are other pieces getting it its way?  etc.

3.
I suppose just 2 squares... although I've never heard the b1-a2 diagonal mentioned in a book (haha) I guess it does exist.

4.
A weak square is a function of both sets of chessmen.  If you have poor or no control over a square that the enemy is able to target that's when it's weak.  The only distinction I would make with weak squares and pawns vs pieces is when a square can never be defended by your pawns (they've advanced passed it) then that square is inherently weaker than other squares in your position.  Whether that particular square matters in a given position or if your opponent can even pressure it has to be judged in each individual position.

5.
Both are fine.  In books I usually see "solid position" when an author is describing a position where the opponent's likely tries for an advantage can be dealt with without complications.  By its nature such a position will, I imagine, almost always involve very few undefended pieces/pawns.

Much appreciation for the responses!

My rule of thumb for selecting rook to move is to plan both rooks. Pick which two files you want your rooks on, and then you know which rook has to move.

Of course there are many many exception and additional considerations,  but that principle might work as a starter.

1.  The question of "which Rook" is one which sometimes even baffles GMs.  Sometimes the obvious answer is wrong because one of the Rooks may be needed later where it is, so if it takes the file, even though it is well-placed ON the file, it has left its ideal position as the game develops.  So, as with all such questions, "it depends on the position!"

2. You probably use both at every turn.  The "elimination" may be subconscious, based on experience and intuition, as waffllemaster notes.  Typically you will quickly "eliminate" most moves and settle on two or more candidate moves, which you then "compare."

3.  As NimzoRoy points out, even 2 squares are a diagonal.  Usually the longer a diagonal, the more important and influential it can be - but again, "depends on the position."

4. A square on your side of the board which can no longer be guarded by a pawn is technically "weak," but not all such weaknesses are significant.  Usually the most important weaknesses are those near the center or your King's castled position - but not always! "Depends ... etc."

5.  Typically a "solid" position is one without glaring weaknesses, one which is difficult to successfully attack.  Not every piece or square need be defended, as long as they are not readily accessible to attack.  Chess involves trade-offs, though, and sometimes a solid position offers less in the way of dynamic chances.

As Fischer said, "To get squares, you gotta give squares."