Yep, progesterone stops ovulation.
No, it doesn't directly affect your future fertility. If you have untreated chlamydia etc for ages as a result of not using condoms, you can have fertility problems.
This 'I'm not having periods, that feels wrong' is why the combined pill has a week-long break, so that most women have a withdrawal bleed. As the progesterone only pills have to be taken continuously, any bleeding is more random / doesn't happen at all.