Hello, how can I check which fares are available for a certain trip and how do I determine the likelihood of upgrading with points? I want to prevent spending more on an upgrade-eligible fare (Essential or above) and not being able to upgrade with points. Thank you in advance.

I suggest that you use a TA to create a booking and hold for you while you call CX to check the upgrade availability.

Hard to say in advance but using miles to upgrade can be done at any point up to boarding. You can ask at the check in desk even and if there's space they will almost always accept miles for upgrade at that point. Often in advance it's difficult but last minute it becomes possible.

The key thing is that you can only do this if your fare class allows upgrade to begin with.

On long-haul sectors, trying to get an upgrade at the time of initial booking itself is not so likely. It may show up at some later point in time. For short haul it's easier.

Another way to check is to see if a full mileage redemption is available in the upgraded class. If it is, then an upgrade redemption should almost certainly be available too.