Marking a batch of photos one at a time is tedious and produces inconsistent results. Doing them together fixes both problems.
A small mark in the corner is easy to remove with a crop, which makes it decorative rather than protective. If the point is to deter reuse, the mark needs to sit somewhere that cannot be cut away without ruining the picture.
There is a real trade here and it is worth being deliberate about it. A mark large enough to be useful is also large enough to be intrusive, and a mark subtle enough to be invisible protects nothing. Decide which you want rather than splitting the difference badly.
Use a transparent PNG. A logo on a white square puts a white box on every photograph, which looks like a mistake because it is one.
Yes, text works the same way and is often more legible at small sizes.
For photos of the same shape, yes. Mixed portrait and landscape sets are worth checking individually.
No.