Welcome to the forum! First, I would never, ever, ever go to a Honda Dealer for mechanical work other than warranty or recall. That service writer is a salesman, not a mechanic, and his job is to see how much he can dig out of your wallet. He will charge a bunch for diagnostics, then charge outrageous prices for parts and labor on things you don't even need. You should have a reliable local mechanic you can trust, and go to them. On the A/C issue: How many miles are on your car? This could be a relay, or a clutch issue, or a clutch coil issue, or an A/C cooling fan issue, or any number of other issues that are relatively inexpensive and easily repaired. Have your guy check the system. He will look to see if you are low on gas, and if so, test for a leak. This system only holds 1.08 pounds of gas, which is a relatively tiny amount, so it does not have to lose much to be low. When it is run low for a long period, that can cause short-cycling (where the clutch is forced to engage and disengage way more often than is normal), which can cause excessive wear or the clutch, as well as the magnetic coil in it, and the associated relays, and, for that matter, the belt, as well. If the system is otherwise good, it could be that your A/C cooling fan or it's sensor is bad. Also, the car's computer may be throwing codes that can help as clues. It sounds like your compressor and clutch are working, though they may need some adjustment or slight work. There are other possibilities, too.
Also, I would post this issue in the Gen3 Section. You are likely to get more replies there. You should also be able to find other threads there on this topic.
Let us know how it goes.