Gosh that's a difficult question. I'm not the right person to answer it, but am posting mainly to give this a bump-up hoping a proper QGD player will take an interest. Not having played either side of this myself all I can bring to the conversation is that you might want to take a look at the QGD games in the five Karpov-Kasparov matches. They at least gave me an outline idea of what led where.
Help me understand some subtleties and ideas in the QGD for Black
In this position I'm trying to understand the differences between White's choices of Bxf6, and Bh4. Are either of these moves more conducive to the exchange variation happening from White?
Bxf6 makes the position more static and will - if black plays b6 - be followed up with cxd5, black loses significant control of the d5 and e4 squares. White will do this to stop black from simplifying with Ne4 that forces simple exchanges. However white must now play actively and accurately to avoid black's superior bishop pair piece formation from taking over and because after cxd5 exd5 black's lightsquare bishop is free. So you only want to play cxd5 if black has played b6 (freeing his bishop to that side anyway) or you can absolutely be sure you can control any movement of that bishop down that longer diagonal (which is possible in the exchange variation but you have to know it).
Weaker players like me make moves sometimes not fully understanding the subtleties of it. If someone that understands the QGD well could help me understand the difference between Bxf6 and Bh4 I would appreciate it.
A lot of good players and even elite players make moves all the time without understanding many subteties properly. It's becoming a lost art because they are just learning off the computer or copying older master games.
In this position with White's last move Rc1, does this signify that White is planning on exchanging on d5 and then playing for the minority attack?
My understanding is that you would choose between either a minority attack or a straight attack down the c-file and not both at the same time. So the rook would tend to move to b1 for a minority attack rather than c1.
Are either the central e4 break plans or the minority attack better in conjunction with either of the Bxf6 or Bh4 moves?
Likely the Bxf6 move, but then your d4 pawn comes under attack.
Another thing I'm not quite clear on is the difference between Bg5 and Bf4. Is this trying to possibly establish a pilsbury knight or something? If so, how do I stop that?
Well Bf4 targets the c7 square while Bg5 is more about central control by pins.
I think c5 should be good in that position. One downside of playing Bf4 is that it you can no longer force black into an isolated pawn formation by the usual cxd5 as black will just play Nxd5 and while in other openings white can play e4 the Bf4 bishop is being hit. White has to play dxc5 to get rid of the threat of cxd4. So c5 tends to be a reasonable choice against Bf4 in general. But normally white waits until the Bf8 has moved to say Be7 so after dxc5 black has to move the bishop a second time to recapture. Here after dxc5 black can develop that bishop and recapture all in one go. It's the exact same situation as how black often waits until white moves the light-squared bishop before playing dxc4 to force him to use up two moves.
1) Bxf6 and Bh4.
The difference is that after 6. Bh4 0-0 7. Nf3 Black has two extremely solid defences, 7... Ne4 and 7... b6. In those lines the black knight usually jumps to d5 or e4, initiating favourable trades for Black as Black lacked space, and the knight is well posted on those central squares. So to avoid these manoeuvers and avoid losing time White can play Bxf6 and try to claim the Bf6 is not a great piece.
2) Rc1.
With the bishop standing on f6 Black has a straightforward way to equalize, by playing c7-c5 to strike at white's center (after say 7. Nf3 0-0 8. Bd3 and then either 8... c5 or 8... dxc4 9. Bxc4 c5 =). The rook manoeuver on the c file makes c5 less effective, and dxc5 becomes an option as the rook covers the Nc3.
3) Bf4 systems.
The bishop points at the black queenside on f4. A typical plan is to play c5 followed by the general advance of the queenside pawns. The bishop performs two useful jobs : hitting the defence squares b8 and c7, and also prevents the normal central reaction e6-e5. The general idea is that in these positions the Bf4 is stronger than the Bc8, giving White a positional advantage.
Black can play c5 before White does, but then White plays dxc5 and Black has weakened several dark squares on which the Bf4 operates.

I may have a different opinion as I play 3. Nf3, 4. Nc3, and 5. Bg5 rather than 3. Nc3 and 4. Bg5, but in my line, White only chooses to play 5. Bf4 over 5. Bg5 if Black plays 4… Be7 as then 5. Bf4 c5 6. dxc5 and now 6… Bxc5 effectively loses a tempo and 5… Bb4 also loses a tempo, while in the 3. Nc3 Nf6 4. Bf4 line, 4… Bb4 and 4… c5 5. dxc5 Bxc5 are Black’s two best replies.

1) Some great questions and you've already gotten some very detailed responses.
I'm a bit of a lazy/practical player so I don't really see much difference between Bxf6 and Bh4 - as I view them as both valid and equal moves. (Given perfect play from both sides they would almost certainly both lead to a dead draw, either way.)
You look at someone like Carlsen, for example, and you'll see that he has played both. He'll pick and choose which move to play depending on his current mood - which suggests that there's no right or wrong choice here ... they both just lead to different middlegames.
2) Regarding the Rc1 move, it's a useful developing/waiting move. White wants to delay the development of his f1 bishop, so that he allows Black an extra turn to consider playing dxc4, so that White can develop his king bishop by capturing c4 with tempo.
Reuben Fine called this "Fighting for the tempo" and suggested many of the moves in the QGD boil down to White trying to find useful waiting moves to delay his Bf1 development, while Black is waiting until Bf1 moves to capture on c4. A back-and-forth battle for tempo.
3) Regarding the minority attack: it's useful to know about, but I'd say it's too early to be thinking about that at this time, as Black hasn't committed to a Carlsbad structure yet (he might end up putting his pawns on b6 and c5, instead).
4) In response to the Bf4 move, I would probably challenge the bishop with ...Bd6 and just "play chess" from there. (Like I said, I'm a bit of a lazy player. )
Weaker players like me make moves sometimes not fully understanding the subtleties of it. If someone that understands the QGD well could help me understand the difference between Bxf6 and Bh4 I would appreciate it.
A lot of good players and even elite players make moves all the time without understanding many subteties properly. It's becoming a lost art because they are just learning off the computer or copying older master games.
Chess is too hard for anybody to understand _all_ the subtleties. Most of the time during the game we are making educated guesses. But the more educated we are, the better our guesses become.
Check out Matthew Sadler (2000) Queen's Gambit Declined. It won a book of the year award when it came out. QGD variations might have changed since then, but the structures and themes are timeless. I wouldn't try to read it cover to cover at first. Just find some relevant discussion for your question (it's in there), and later when you have more questions go back to the book. Elsewhere Sadler relates he had a lesson with Dvoretsky, who taught him about black's defenses in the Carlsbad / Exchange line. And then Sadler put that in his book. Books are how chess knowledge is passed from one person to many.
I know this is probably a bit advanced but I would really appreciate the help!