First time will be JFK-LHR-CPH, with a 6hr layover during which I would like to lounge hop in T3, then eventually return to the CCR in T5.
How’s the liquid situation over at T3? And will I need to go through security again when I come back to T5? If so, better to go through the First Wing or transit security?
The second time will be on the return CPH-LHR-JFK, where I will be staying in T5. Again, am I better off clearing transit security or going through immigration and then the First Wing?
It's CT scanners at both T3 and T5 Flight Connections, so liquids need to be under 100ml, but they can be in your main bag and they don't need to be in a ziplock bag. There are only a few legacy scanners in T5 now, but in theory you should prepare for the risk of ending up with a legacy scanner.
Accounts vary as to whether you will be allowed to lounge hop in T3 - boarding passes are scanned there and some people are allowed through, others are not. If you are denied entry you can take the bus back to T5. But you would get scanned in T3 and then again in T5 if you did get through,. Most regulars, self included, will use the First Wing over Flight Connections, which you can do in both directions, so long as you have about an hour before your next flight. First Wing is only CT.