It's a lot easier if you have a specific example (flight #s especially useful), because there isn't really uniform advice especially for your second question.

First question: Make sure when you check-in at the first airport, they link the two PNRs. Once you do that it doesn't really matter IME if they're separate or the same if they're both on CX metal. But the bigger point here is your first question isn't really relevant or basically misses the point, because your Q seems to implicitly assume connected PNRs get "waited for". You, the individual passenger, are really just a very tiny variable in the whole process to wait or go. Just as one example, occasionally CX will strictly enforce the MCT on CX-CX itinerarites when it comes to arrival delays. Meaning, let's say your itinerary was originally a 90 minute connection. But the first flight is 55 minutes late, so you arrive with only 35 minutes to connect. Physically-wise, aka transit security and running to gate from virtually anywhere in HKIA to anywhere else, it's almost guaranteed you can make your flight. But practically, we've seen CX play hard ball with these situations (occasionally) before and say "due to your arrival delay, you missed the MCT and we've already re-booked you on the next flight. Here's your new BP" In this case, our speculation is CX has almost certainly already given your seat away, because they needed the seats on your second flight perhaps for an overbooked scenario, IRROPS on other flights, etc. They were in need of seats and could squeeze you off due to a technicality.

It's true you have a better chance of being "waited for" if you're, say a group of 30 people. But one or two folks, once your PNRs are linked don't bother worrying if they flight is waiting for you or not. It's up to the Gods if you land under the MCT. *I have never experienced a case like the one I've outlined above, and have transited HKIA numerous times under the MCT.* But we read about situations like this on here.

Second question: Please provide more details. The situation is different if you miss the once-daily flight to Manchester, versus if you miss one of the 15 or so daily TPE departures. And it depends how you bought your ticket. Quicker, more convenient and comfortable options will open up if you're on a cash ticket. But generally CX is good with irrops. Reports on here for the less-frequent departures include paying for hotels, or routing via other cities on the next available flight.