My intuition tells me to use a low gear and press heavily on the accelerator to see if the revs increase suddenly. If they do increase suddenly, the clutch is probably failing. Is this intuition correct? Or would it be better to do the test using a high gear?
Basically correct, but you'll see/hear the slippage much better in a higher gear than a lower gear. Roll your car at about 20mph (25kph), put it in a higher gear than you normally would (something like 4th gear), release the clutch and punch the gas. If the engine spins up faster than you'd think (the engine/vehicle do not speed up as one, but rather the engine speeds up without seeing much of speed improvement in the car), your clutch is slipping.
How sudden is the clutch failure?
If you are just talking about it wearing out, it will usually take some time for it to occur. This could be a couple of weeks to a couple of months, depending on how the car is driven. If there is a mechanical issue with the clutch, then obviously it's going to happen fast.
So, can I safely drive back home and to the garage after I have observed the clutch is failing?
I would think you usually could do this, but it really depends on the shape of the clutch. If it's been slipping for some time and you haven't noticed it, it could already be in bad shape. Just remember that a slipping clutch will self destruct sooner or later. Also, the greatest thing which destroys a clutch (to include the flywheel) is heat. The slippage will cause greater heat, so as it slips more, it will destroy itself faster and faster. IOW, it's not linear.
Is it possible to drive the car normally while waiting for the reserved clutch job time in the garage for, say, 500km?
It really depends on what "normal" means to you. If you are in a hilly/mountainous region, you'll experience a lot more wear than if everything's flat. If you hotrod you vehicle, you're going to see faster wear. If you really baby your clutch, yes I'd think it could be possible. Just remember, if the flywheel is in good shape now and you continue to drive it, you'll most likely either need to have it resurfaced or replaced. (NOTE: You'll at least want it burnished when you get it changed ... make sure they do at least that during the replacement.)
If a car with failing clutch is driven, is there a risk that something very expensive breaks?
Nothing beyond the clutch assembly and flywheel. The clutch is fairly much self contained in that it is only a coupling device which connects the engine to the transmission. When it goes out, it just quits coupling.
My understanding is that the remaining life of a clutch cannot be observed without taking everything apart. Is this correct?
That has been my experience.
Are there any cars with a clutch wear indicator that would allow easily seeing the remaining lifetime of a clutch?
None that I'm aware of ... you used to be able to adjust your clutch cable and that would be one indication your clutch was going south. With hydraulic clutch release mechanisms, they self adjust so you really don't know.