How many times can I reuse coffe-grounds to make myself a coffee until it is tasteless/useless or has no properties at all?
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.
This is a somewhat subjective matter. It is known that you dissolve around 15% of the ingredients in a coffee bean at first brew. However, this 15% seems like the best portion of it.
Another approach could be using percolators. By design, percolators reuse grounds over and over during brewing. So, you can dissolve a higher percentage of solubles with a percolator which fits your taste. If you don't care about the coffee to be more bitter, then you could go beyond 15%. As a result, you can use less grounds for the same amount of coffee. Actually, during instant coffee production this is what producers do. They brew less grounds for longer periods and end up bitter tastes.
Please see the following discussion on percolators to see how they work: