]And am I right in thinking there are more questions in the beginning, and less as the play progresses?

I thought so too, until I took a close look.

First, my formatting had some problems, so the count isn't exact--although it's within ten questions or so.

In general, the number of lines over all per act seems to be the dominant factor: I=70, II=75, III=95, IV=60, V=90.

Act III is the longest act.

Act V, more than half the questions are in the first scene (the gravedigger/burial scene) and most of those are meant for comic effect. The riddling nature of that scene rather throws off the pattern, perhaps, but it's very interesting that that particular scene has more questions than any other--even the first scene of Act III, which contains "to be or not to be."