Fiducial placement

You've got answers to most of your question, but I'll add more detail on this one part,

If you have 2 fiducial on the board and you add 2 more close to a fine-pitch component like a BGA or a big QFN, why doesn't that violate the "3 fiducial maximum" rule?

What you call the "3-fiducial rule" is really "Don't put fiducials in all 4 corners". The reason is that if there are fiducials in only 3 corners it's much easier for the vision system to detect if the board has been loaded in the wrong orientation, rotated 90 or 180 degrees from the way it's expected to be.

(Why your vendor is okay with 2 fiducials in opposite corners, which has the same problem, I'm not sure. The vendors I work with prefer fiducials in 3 corners)

Additional fiducials in the middle of the board (near fine pitch parts) don't create unwanted symmetry in the fiducial arrangement so they don't cause problems.

The most qualified to answer your question is the EMS that has to assemble your PCBAs.

Usually it is at least 2-3 fiducial marks. I don't think there is an upper limit to how many marks you can place. The EMS will just ignore them if they don´t need them.

The fiducial marks are used for alignment/registration of the pick'n'place machine. I usually place a few (4 or 5) on each side of the PCB (depending on the size).

There is no problem for the machine to place components in the "A" region of your figure.

In your last figure I would place on near the point of the arrow.

You need to check with the company that places your components what the requirements are but typically you will have three to allow for the artwork being slightly over or undersize and for the artwork being slightly rotated in relation to the PCB. These should have a clearance in the solder resist around them to ensure the machine locates on the copper and nothing else. In addition you may require local fiducials around fine pitch components but these may not be required if the board is small enough that the main ones suffice.

For panels of small boards I have often placed the fiducials of the break-off region instead of each individual artwork to save space.

Fiducials are not usually required for boards consisting of Pin Through Hole (PTH) components only or hand built boards and if you have surface mount on both sides of the PCB they are required on both sides.

Note: too many fiducials is not a problem as the board-stuffer will just ignore any they do not need.