Some simple things to do to it that will make it quicker is change the injectors to bigger ones(400cc),change the fuel rail and upgrade it to a aem fuel rail,bigger throttle body,header but that will cost about 3 grand so it would be alot more easier to just save your money up for a rsx type s or a gsr integra but its your call and with the ac on it should stay around 800 rpm at a idle and it shouldnt go below tht you should take it to your local shop and get all your hoses flushed and make sure you dont have any blockages anywhere in your hoses after you do that you should be good to go does your car have a check engine light on?
How would bigger injectors, an upgraded fuel rail, larger throttle body, and a header make the car quicker when it also has stock cams, intake manifold, intake piping, cat, exhaust, and ecu? Doing only the things you stated will see no performance gain and cause the car to run worse than it normally would. Even if he were to get the car tuned after the gains would be miniscule because he has no other supporting mods.
And taking your car to a shop to get the hoses flushed probably won't do anything to fix his idle fluctuation except waste him money. He should look into some of the common causes of the fluctuating idle, such as a dirty IACV, and work at those.
OP: When I have the A/C on in my Miata, the idle will fluctuate from normal idle (~750-850) to a high idle (~1300) as the compressor is turned on and off and the extra load is put on the engine.
One of my Integras had working A/C for about 8 hours one day after a recharge, and when the compressor clicked on the idle dropped from like 700 to like 200 and almost stalled, then jumped up to about 1500. This was the first time the compressor was on in years. The idle would fluctuate as the compressor turns on and off. The A/C condenser fan should also turn on when the idle changes.