Security is done at the gate in Singapore, so yes you will need to clear it. And you will need to move between terminals, which you can do airside. I'm not sure what the official MCT is, but 90 mins should certainly be enough, for example.
CX and SQ are definitely in different terminals. I believe CX comes into T1 and SQ flies out of T3 - you can check by google Changi Airport to confirm.
There is a skytrain that can get you btw terminals and they run every few minutes. If you don't get your SQ boarding pass in HK, there are transit desk at each terminal.
You do not need to exit the terminals as each gate has their own security checks. Lines are not long and you can do the entire change in under 30 minutes from time the doors open on your CX flight (maybe extra 10 minutes to get SQ boarding pass).
Security is done at the gate in Singapore, so yes you will need to clear it. And you will need to move between terminals, which you can do airside. I'm not sure what the official MCT is, but 90 mins should certainly be enough, for example.
You will only be clearing secrity not immigration, I would be happy to do it in less, the train seems to go continuously, it's a lovely airport, and the SQ lounge is well stocked. My advice is to allow yourself a little extra time, stretch your legs after the flight in Y, pamper yourselves a little in thelounge, regards bkkrop
90 minutes is more than enough time. Changi Airport isn't like HKG or NRT - when you deplane, you go straight into the airside gates and can mingle with the other travellers waiting for their flights instead of going to some queue for security screening before going to the airside waiting areas. In this sense it's exactly like US airports on the domestic side.
As for gates, you should find out clearly which terminal and gate your SQ flight is departing from as soon as you get off the CX flight. SQ departs from either terminal 2 or terminal 3, but the actual decision of which terminal/gate is usually not made until about 2 hours before flight time.
Don't worry about making the transfer. Changi is a seriously organized airport, the place runs as reliably as a Swiss watch.
