Won't start Had worked fine- 3 hours later - won't start. Makes clicking sounds, then different sounds. After a bit, the lights will come on, door alarm etc. Checked all the fuses - no problems - battery seems charged.

The symptom you describe of starter clicking, sure does sound like a weak battery.
The starter draws 120-200 amps and if down a bit, the battery will not supply that kind of current.

The other loads you mention are puny by comparison only requiring a few amps and can be tolerated by a tired battery after it has a while to recover from the starting current it tried to deliver.

Even with a jump, don't get too far from home; the alternator may be at fault and not charging the battery as it should.
There is a kind of failure that can happen internally in the alternator that will drain the battery.
The only way to determine if this is the case is by monitoring the current drawn from the battery with everything that can be turned off, turned off.
All modern vehicles draw some kind of current even with 'everything' off. The computer, clocks, certain radios, all these things draw minute currents even when not in use but the total drain should be well under an amp.

About any cheap digital meter has a 10 Amp UNfused input that is handy for checking this drain but if it exceeds the 10 amps, it will likely damage the meter. Once the battery is disconnected, just tap the leads to see if it appears the maximum will be exceeded. This short term high current won't bother most.
DON'T turn ON anything while doing this, lots of things in a car draw >10 amps.

If you have a Harbor Freight tool store nearby, they often have adequate such small meters for ~$3.
Otherwise, Radio Shack.