1) If playing with split broadsides, when does a vessel strike? Is it when one broadside reaches zero, or both? (We assume one - if either broadside reaches zero then the vessel strikes).

Your assumption is correct - when the first broadside reaches zero.

2) A vessel with a mast over the side (or one that is fouled) drifts in the first command phase of the turn. It then, either in that command phase, or its own, gets to roll to cut free. If it does so can it then move in the ensuing action phases, or does that fact that it has drifted negate all movement for the turn, even though the vessel is no longer hindered? (We still aren't sure about this one - we allow the vessels to move).

Again you are correct - if you cut away the mast you can move as normal in the following action phases.

3) If a vessel loses a mast in or before its first action phase, and that mast fouls, what does it do for the rest of the turn? (We assume that it cannot move for the rest of the turn, although it does not drift until the start of the next turn.)

Again correct - the ship is immobile and then tests for cutting the mast away or drifting in the next command phase.

4) How are chasers lost to gunfire? (We assume that a rake will apply damage to chasers as well as both broadsides, but that a shot from elsewhere will only damage chasers if 2rr or greater is scored, in the same way that the 'opposite' broadside is damaged.)

I admit this is a bit of a grey area, but I'd probably have them lost only to rakes (there weren't many guns involved - 2 or so at each end of the ship - and a heavy broadside hit would, I think, be less likely to KO a chaser than guns and crews on the opposite side.

5) If a vessel is anchored by the bow it will turn on the anchor until its head is into the wind. If it raises or cuts the anchor, what happens then? (We assume that it spends its first action phase falling off onto either of the two beating tacks).

Yes - the first turn is spent turning into a position from which the ship can move off.

6) What is the Short Range modifier for a gun type 'E' vessel? It appears to be missing from the charts. (We assume that it is '-1')

No - gun type "E" (unrated vessels) only fire out to 10cm (we are generally talking about very light guns). However, if you want to consider unrated ships with larger guns -2 would do at longer ranges.

6) So, what is a "point" then? The rules say 30 degrees but the angle on the Turn Indicator and the tabular wind table are both set up for 22.5 degrees?

Its 22.5 degrees. The number in section 5.6 is a misprint (sorry!)