>> If I want to travel on a cable cars that are fully covered by STP (eg Stechelberg-Gimmelwald-Mürren and Grütschalp - Lauterbrunnen) do I just wave my STP to get onboard? Is using cable cars just the same as taking trains in that respect?
For cable cars, you usually need to go through a barrier gate, which is released by inserting a ticket that can be read electronically. This means presenting your Swiss Travel Pass at the ticket office to get a free or discounted (as appropriate) ticket for the barrier gate.
I'm pretty sure that is the case with the Stechelberg-Gimmelwald-Mürren cable car, as I remember feeling relieved that I would not have to join the ticket queue, when I saw how long it was. I headed straight for the cable car, but was turned back at the barrier gate and had to join the queue anyway, to get a ticket for the barrier gate :(
I'm not so sure about the Lauterbrunnen-Grütschalp cable car, as I don't recall getting a barrier ticket for that one, although there are definitely barrier gates at the bottom, if not the top as well.
In any case, there will be signs in English, so just keep an eye out for them.
>> So if I set off from Lauterbrunnen I can do the Stechelberg-Gimmelwald-Mürren - Grütschalp - Lauterbrunnen loop for free?
Yes, including the bus from Lauterbrunnen to Stechelberg if you decide not to walk.
>> If when I get to Mürren the weather looks nice and sunny and it looks like it is worth taking a look up top at Schilthorn I can just buy a ticket there.
Yes, but if it's busy, that means joining another queue. You could check the Schilthorn webcam before leaving your accommodation/Lauterbrunnen/Stechelberg, and get your ticket for the Schilthorn at Stechelberg if it looks clear on top. If it is clear, I would go up straight away, in case the clouds come in later.
>> Unfortunately I won't be able to take the Allmendhubel Funicular as I just discovered it is out of action (extended maintenance) until 16 June this year. Just as a matter of interest is it covered by the STP? It doesn't appear on the validity map.
Yes, the Swiss Travel Pass gets you a 50% discount. It is on the Swiss Travel Pass validity map, but not easy to spot, as it is just a very short track, and just appears as a black circle (see attached picture), so you can't tell whether it is free or discounted. However, fares for the Allmendhubel funicular with the Swiss Travel Pass can be confirmed on the Schilthorn web site