Some questions:

1) Does anyone have any figures for commonest causes of failure? (In
other words, where do I look first?)

Aside from what you've already checked, I've had a number of lamps with
shorted mylar caps in them, other times one of the cathodes will open so
check those for continuity.

2) Are the thermal fuses essential? Not all units seem to have them -
at least that I can identify. Whilst I'm not one to go removing safety
devices willy-nilly, more recent units do seem to have slightly lower
component counts, fuses included in some. Should I fit thermal fuses to
ones that don't have them?

Some have fusible resistors instead, if there's any sort of protection,
replace it for sure. If there isn't any it wouldn't hurt to add a low value
fusible resistor but they should all have something.


3) Are these devices sensitive to spikes/surges and, if so, should I put
MOVs in any that I repair?


Not worth it, the MOVs will cost more than the lamp generally.

I know that these only cost $5 AUD each, but there's a principle at
stake here...


Exactly, I *always* try to repair them when they fail, it's a simple
excercise if nothing else.