I realize that it's hard to give general guidelines here, since every chess position has unique considerations. Still, any rules of thumb would be appreciated. I would rather be right 80% of the time than fly blind and "flip a coin" on these decisions every game.
If he ignores your pin by castling / moving queen / interposing the bishop, you have 2 options : exchange or keep the bishop.
I would prefer to keep the bishop, but then you need to put pressure on pieces / squares that are connected with the pinned knight. Pressuring the center ( e4 / d4 ) is always good. This way your bishop remains useful even after White breaks the pin.
If you decide to exchange, remember that in endgame, bishop is superior to knight ( my answer to this question is instructive regarding bishop vs knight debate ).
Still, many openings ( like Nimzo-Indian ) are viable even after the exchange of bishop for a knight. Equality is reached by creating swift action by opening the game for the knights. Why? Because knights are better positioned in the early game then bishops since they are centralized in one move. while bishops need lots of maneuvering to get ideal squares.
Furthermore, by exchanging the bishop for a knight, you remove your piece that made 1 move for his piece that made 1 move, but in order to recapture he needs to play with the same piece twice while you get the chance to introduce new piece. This gives you development advantage, so it is logical to open the game.
In short, if you exchange be ready to start swift action. If this is not possible, you must get some compensation ( like better pawn structure, development advantage... ) or else White will favorably position the bishops and open the game with devastating effect.
As for "putting the question" to the bishop, again you can exchange or keep the bishop. If you exchange, then proceed as I have described above. Otherwise you can maintain the pin or reposition the bishop, but the principle is the same as above: if you can pressurize points / pieces connected with his pinned units, maintain the pin ( but always asses the consequences of g4 push! ) otherwise just reposition the bishop to a better square. He did lose a tempo and has weakened himself with h3 so you have time to play twice in the opening with the bishop.
I understand that all this might be abstract, so here are some illustrative diagrams that should help you even further:
[Title "Bishop exchange that speeds up implementation of a plan"]
[fen ""]
1.d4 d5 2.c4 e6 3.Nc3 Nf6 4.cxd5 exd5 5.Bg5 Be7 6.Qc2 O-O 7.e3 c6 8.Bd3 Nbd7 9.Nf3 Re8 10.O-O Nf8 11.h3 Ng6 12.Bxf6 Bxf6 13.b4! a6 14.a4
This example illustrates what to do when opponent breaks the pin -> just stay calm and play in such a way that bishop move becomes useful. Again, as I have said before, the pin usually puts pressure on the center ( here on d5 pawn ), and simply pressuring that point will justify the bishop's position even after the pin is broken. Notice how White got extra move with the exchange to start fast minority attack: without Bxf6 Black's dark square bishop would prevent this move so White would have t play a3 first in order to get b4.
[Title "Putting the question to the bishop"]
[fen ""]
1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Ba4 ( 4.Bxc6 dxc6 5.O-O f6 ( 5...Bg4?! 6.h3! Bh5? 7.g4! Bg6 8.Nxe5 Bxe4 9.Re1 ) 6.d4! exd4 7.Qxd4 ) 4...Nf6 5.O-O Be7 6.Re1 b5 7.Bb3
Again a good example that shows that you don't have to exchange the bishop just because the pin becomes ineffective. This example requires explanation.
First of all, notice that it is possible to exchange the bishop, and notice how White makes swift action in view of rapid development and opening of the game. Furthermore, notice that White got compensation in view of better pawn structure ( he can create a passed pawn on the kingside, Black can't ) so this will diminish the power of bishops in the endgame. This is the application of the same principle as above.
The sideline with ...Bg4 illustrates well my warning that you must always evaluate consequences of g4 push in such positions. Black had no time to maintain the pin and should have exchanged the bishop.
Now, in the main line White was able to maintain the "pin" because ...b5 push was favorable for him ( b5 pawn is a weakness and White bishop will retreat to a good diagonal ). If you study theory of this line you will see that ...b5 move is forced because the pressure on e5 pawn is strong. Again, this confirms my principle of just putting squares / pieces that are connected with the pinned knight under pressure.
Here is an example that puts everything pretty much together:
[Title "Black applies almost all the above principles to reach a draw"]
[fen ""]
1.e4 d5 2.exd5 Qxd5 3.d4 e5 4.Be3 Nc6 5.Nf3 Bg4 6.Be2 O-O-O! 7.Nc3 Bb4 8.O-O Bxc3! 9.bxc3 Nf6!? 10.c4 Qe4 11.Bd3 Bxf3! 12.gxf3 Qh4 13.d5 Nd4!? 14.c3 Ne6! 15.dxe6 e4! 16.fxe4 Rxd3 17.Qxd3 Qg4+ 18.Kh1 Qf3+ 1/2-1/2
This example is one of the main lines in the Scandinavian defense, and is taken from the book C.Bauer-Play the Scandinavian ( 2010 ).
First crucial moment is 6.Be2. This is the moment that troubles you, right? Well, look what strongest GMs do here: they put pressure on the squares / pieces that are connected with the pinned knight ( ...O-O-O! ). This example clearly illustrates the connection between the pinned knight and the center, and why it is more important to pressure the center then to rely on a pin that will be short-lived anyway.
Now comes the second momment that illustrates second type of position that troubles you: bishop pins the knight against the king ( 7...Bb4 ). What happened here? White castled, and here we must analyze the position thoroughly so we can understand why 8...Bxc3! was played.
Black could try to move the queen and preserve the bishop, but in this opening everything revolves around development advantage. White has already finished development, has strong influence on the center and will probably force Black to relinquish the bishop pair ( these guys are deadly in open positions like the one in the game ). Black on the other hand needs one more move to finish development, and he needs to maintain the pressure on White center. Moving the queen would loosen the pressure and give White time to start regrouping for an attack. That is why Black decides to exchange the bishop -> he gets extra move so knight on g8 can enter into play, he weakens White's control over center and claims e4 square for himself and gets healthier pawn structure that diminishes power of the bishops in the endgame.
I just wanted to say that you need not fear when opponent ignores your pin by castling / moving the queen or if he breaks it by interposing the bishop -> just keep playing and put pressure on the squares / pieces connected with the pinned knight, or simply exchange and start a swift action.
The last illustrative moment starts with 11....Bxf3! and here we again see the concept of exchanging the bishop to get time for a swift action and to ruin opponent's pawn structure.
Another concept is illustrated, and I have mentioned it earlier, and that is the opening of the game in order to exploit the knight's speed over bishops. Notice how strong and well posted are Black knights, while bishops were not posted on their best squares. Notice how Black got slight initiative after 13...Nd4!?, although it was only good for a draw.
I think that these examples cover all 3 cases that troubled you, in both positions you mentioned so if you have further questions leave a comment.
Hope this helped, best regards!
g4push does create holes! ) you can always reposition it to a better square. It costs you just one move, so as soon as you finish opening, you can reposition the bishop. It is "low-cost" waiting move, and is almost always useful. Exchange only if you must, or you see concrete profit from it.