If I buy a Passthrough share, do I receive some of the BTC the company mines? I'm not expecting miracles, though, like ROI in a month or such (especially that I couldn't really buy more than 1 single share, which I guess is considered ridiculously few), but still I'm interested in the concept - is it somehow like a mining contract?
Yes. In the order of 95% of dividends are paid through the PT shares. But do your own research to be sure.