Above ideas by Barky and knfen good place to start. Some other ideas … the engine computer may increase the idle speed when the A/C compressor is engaged, to prevent stalling. The idea is that the compressor loads the engine enough to reduce the rpm, and the bump in rpm just compensates for that, keeping the rpm steady. Maybe the computer thinks the compressor is engaging when it actually isn’t. Due to a faulty “clutch-engage” sensor or something. That could cause the engine idle speed to increase intermittently when the AC was being used.
If the compressor was starting to fail , binding up, and causing extra load on the engine beyond normal when engaged, that’s a possibility too.
On the evap leak, the engine computer may occasionally pressurize the fuel tank , purposely, then monitor the pressure vs time, to test for evap leaks. So if the pressure sensor was defective, that could cause the computer to think there’s a problem when there isn’t. There’s an evap-related valve at the top of the gas tank in many cars that can fail and cause this problem too I think. Of course if any vent hoses are leaking, that’s another possibility.
On the leak, my guess it is coolant, which indeed feels slick. The brownish stain is probably just rust getting into the drip as it slowly leaks over the iron engine components. This needs to be diagnosed by a shop to know for sure, but it might be the water pump is starting to leak a little from its seal, or just a hose connector isn’t quite tight enough, thermostat gasket starting to fail, etc. Probalby something minor but needs to be properly diagnosed at least. You may decide after figuring out what it is and knowing it isn’t serious to let it go awhile and just keep the coolant topped off.