Unless they've changed, the Honda professional engines GX120, GX160, and GX200 use separate choke and throttle (governor) controls. Correct starting procedure is to open fuel petcock, set choke to "closed" position, and set throttle (on the handles) to about 1/2 way. Ignore the "Choke" markings. Tru-Cut uses a generic throttle cable and level. Most engines (like Briggs) have an integrated choke and throttle. When the engine fires, back off choke to 1/2 and let run for another 30 seconds until it smooths out and then turn choke off. The throttle control should permit any speed between idle and maximum governed speed (about 3300 rpm). Appropriate speed for mower is as fast as you can comfortably follow and control the mower. Generally a faster engine speed spins the reel faster producing a better cut, and throws better into the basket. There is no right or wrong speed. It depends upon your comfort level and your ability to control the mower. Only caveat is not to run so slow that you lug the engine, and it won't pull properly with reel engaged. There are differences of opinion on this forum, but for me best shut down practice is the close the fuel petcock and run engine at idle or 1/4 throttle until it dies from lack of fuel. This gets rid of most fuel in the carburetor, reducing the amount left to evaporate and turn to varnish. Honda also has drain screw on the float bowl of the Keihin carburetor, which you can remove to get the gas out. I would use the drain screw and treat the gas in the tank with Stabil for off-season storage.

Man I hate to see cultural animus in a lawn site thread but some people just can't help themselves. Anyone driving an Anerican owned (that's right, I didn't say made because for anyone that doesn't know it Toyota has the largest percentage of US sourced parts and labor. Not Ford Chevy and especially not Dodge) can mainly thank Honda for bringing providing us with their superior engineered and produced vehicles that simply forced the US brands to step their game up. Anyone that says with a straight face that they have owned US and Japanese cars and had more issues with the Japanese vehicles is either horribly unlucky or is lying through their teeth. 20y ago there was no comparison between the two, from NVH to the blatant lapse in QC that allowed vehicles with panel gaps so large to leave the manufacturing facility that when one took a 88 Dodge Aries k down the highway it sounded like there was a wind machine blowing in the back seat. Give me a break. The engine tech on Honda machines are superior in myriad areas. They are much quieter, produce less emissions (don't let the fact you don't believe in climate change stop you from worrying about it...), more efficien power production and because of that much,much, much better fuel economy. On my old snapper with a Briggs mower I would seriously have to refuel once during each mowing session (that mower would have been ~14y old if it were still functioning) and now with my ~9y old HRT with the GCV160 I can almost mow my lawn twice before refilling and yea, the tanks has commensurate capacaties. That's almost a 400% gain in fuel economy. Doesn't take a brain surgeon to see that glaring advantage. The Briggs was about as hard to start as you could imagine, that's what caused me to kick it to the curb. The last stint of pulling the starter cable for 5m, foot on the deck sweating my you know what's off sealed the deal ( I'm not a tiny guy either 6'1" 190). My Honda has started first pull everyone in the 5y I have had it and this is a sissy pull pretty much just using my shoulder and arm strength. I'm sure there are some older B&S out thee that are freaks and just won't die that start first pull everytime but the fact is that is the exception and simply not the rule. If there is one weakness of the Honda mower it would be the carb. But if you don't let stale gas gumm it up and properly maintain the machine (IMO anyone that does not maintain their machines according to the factory guidelines should not be allowed the gear pleasure of caring for their lawn, it's ignorance of the highest degree).

The A/C relay on your Honda, like most vehicles today, is computer controlled. The relay will have electrical power at two terminals of the relay with the key on and power at only one terminal with the key off. If there is no electrical power present at the relay, then you have to inspect the fuses. There are two fuses for the relay. One can be found in the under dash fuse panel. It will be a 7.5 amp fuse and will be located in position #6 of the fuse panel labeled A/C clutch relay/cooling fan relay. The other fuse is located in the under hood relay and fuse box. This is a 15 amp fuse and will be in position # 34 and labeled condenser/fan. If both fuses are good and there is electrical power to two of the terminals at the A/C compressor clutch relay, then you have a control problem. It could be as simple as a bad relay or the A/C system is low in charge. The A/C system has a pressure switch that stops the operation of the A/C compressor if the charge of refrigerant in the system becomes inadequate, too low. This is done to prevent damage to the compressor. To diagnose a control problem will require more specialized equipment, higher level of training and knowledge for diagnosis. At this point I would suggest that you involve a repair facility to perform this diagnosis.

What switch is it? There are a lot of switches on an A/C system.