I hope you don't get bored by all those positions and analysis. I actually find it very exiting! I feel we are making steady progress, albeit slowly.
My list with positions where I want to learn to
see the solution in stead of just to calculate it, becomes slowly shorter. Meaning that it is indeed possible to replace
calculation by
seeing. I'm in no hurry, and I take my time to grasp every detail of a position, trying to devise some rules that can be applied in other positions. I'm not interested in the very position itself, because most details are accidental, and hence limited to only that single position. I'm only interested in the details of the
combination. What makes that the combination actually works? Why does it gain wood? I make little changes to the combination, trying to keep everything else the same. I add or remove pieces, and see how that influences the outcome of the
combination, while ignoring the effects on the
position. I change the move order and see what difference that makes. I use Stockfish to check my conclusions.
The following position is about removal of the guard.

Diagram 1 White to move 
r1qr2k1/pp2ppbp/1np3p1/4P3/2b1PP2/2N1B3/PPQ1B1PP/3R1RK1 w   1 1
Solution
The black knight protects the bishop. I realized that removal of the guard by
1.Bxb6 only works because it threatens the black rook on d8. It is a multi purpose move. A capture plus a threat.
Let us see what the effect is of removing the possibility of this threat. Does the combination still work? In order to find out, I removed the black rook on d8. In order to keep the material in balance, I removed the white rook on d1 too. We get the following position:

Diagram 2 White to move 
r1q3k1/pp2ppbp/1np3p1/4P3/2b1PP2/2N1B3/PPQ1B1PP/5RK1 w   1 1
Now the combination doesn't work any more. Since 1.Bxb6 doesn't threaten the rook, black is no longer obliged to take back on b6 first. Black has time to get rid of his problem bishop by playing 1. ... Bxe2
This leads to the following
Rule: removal of the guard only works when it is a capture which gains a tempo.
In this case, by a threat.
This rule probably can be generalized:
Rule: look for captures which are accompanied by a threat.
I asked myself whether it is necessary to threaten a piece of higher value. So I decided to replace the black rook by a knight. Adding a white knight on b1 for material balance. I saw that 1. ... Bxe2 threatens the rook on f1. For clarity I decided to remove the remaining rooks too:

Diagram 3 White to move 
2qn2k1/pp2ppbp/1np3p1/4P3/2b1PP2/2N1B3/PPQ1B1PP/1N4K1 w   1 1
The combination still works. This leads to the following
Rule: look for captures with follow up captures
What happens when black has a follow up move too? I replaced the white knight from b2 to f1:

Diagram 4 White to move 
2qn2k1/pp2ppbp/1np3p1/4P3/2b1PP2/2N1B3/PPQ1B1PP/5NK1 w   1 1
Now the combination no longer works. If both sides have equal follow up moves, removal of the guard doesn't work.
Rule: you need one follow up capture more than your opponent
Giving black more than one follow up possibilities doesn't change the outcome. The one who started with the first capture can decide to break off the series of captures whenever he wants.
Rule: only the one who starts the series of captures has the chance to win a piece. He wins a piece when the opponent runs out of captures.
Does the move order make any difference? In diagram 1 there are 3 possible captures:
The last capture shouldn't be considered as first, since it is a capture without a follow up threat.
What if white plays 1.Rxd8+ Qxd8:

Diagram 5 after 1.Rxd8+ Qxd8 white to move 
r2q2k1/pp2ppbp/1np3p1/4P3/2b1PP2/2N1B3/PPQ1B1PP/5RK1 w   1 1
If white now captures the knight on b6 with 2.Bxb6, then black can take back with 2. ... Qxb6+ and the combination doesn't work due to the check. But that should be considered an accidental feature of the position. If the king had been on h1, the combination would still work!
What does this tell us? We have to look for captures with an additional punch first. The winning tactical theme here is removal of the guard. Worries include the possibility for the now unprotected black bishop to counter attack. It becomes a desperado.
Other captures than 1.Bxb6 that have an additional bite, are
in general equally well playable (=1.Rxd8+) without changing the outcome of the main tactical theme (removal of the guard). In essence, such captures with extra bite are
postponement moves. They
postpone the execution of the tactical theme by one move, since they require immediate action. You can play an infinite amount of postponement moves, but the main problem for black remains.
It is important to grasp the main ideas of the position, to reduce you calculations. But you still need to calculate every line. Since there might be a capture with a counter bite for your opponent as well that you might overlook. But calculations with a mind that is not already overloaded, is usually no problem.

Removal of the guard 