Booking an award ticket: Paying for Business but only Economy Available

hi, I am sure this would have been asked earlier, but I could not find it here or even on the united website. So have come to my favourite place.

I am planning a holiday, and want to book Business Class tickets on points. The journey involves a connection. Saver awards in business are not available on one of the legs, so it shows up as a mixed award.

Assuming I book that, is it that

(a) I am placed on a wait list for business, but have confirmed economy for that segment.
(b) If not, is it possible that business availability on saver may show up later? IF so what should I do? Cancel/ rebook?
(c) AT the gate, if there are empty seats in business would there be a chance that we could get into business for that segment given that we have paid for business.

Would your answer be different in case

(1) I was flying United
(2) I was flying a star alliance partner for that segment.

So many factors to consider! In my case, if I am willing to accept a (significantly) longer stopover, I can get business in both legs. So was wondering whether should book that and then try and change the flight later. Alternatively, should I book ideal connections, and see if I can get into business anyway.

Thanks in advance.