How many times can I reuse coffe-grounds to make myself a coffee until it is tasteless/useless? How many times can I reuse coffe-grounds to make myself a coffee until it is tasteless/useless or has no properties at all?
Zero.

when you make coffee, (ideally) all of the desireable solubles get extracted, what remains are, if done well, most of the undesireable ones and insoluble components. A second round of extraction will not produce anything you'll want to drink, unless you like bitter brown water.