4200 is so cheap it sounds to good to be true is all. Theres also about $500 in miscellaneous materials plus a permit coming out of that. Even if it’s like 10′ from the furnace to the condensing unit, 30′ from the electrical panel to the condensing unit, and theres already a slab to put the condensing unit on theres still around $300 misc. A drain line has to be run (of course), the furnace condensate is acidic and will eat metal pipe, concrete, and kill plants. Your metal/ceramic/asbestos combustion gas vent pipe must be completely replaced with a pvc one. I wouldn’t do all that work for 800 bucks but theres always someone hungrier. If your existing thermostat doesn’t have cooling or a 2nd stage of heat, if you need more return air to get the required cfm for cooling, thats not a freebie, thats a required part of the job. Hopefully theres enough insulation on the ductwork that it doesn’t sweat in cooling.
As far as licensed and bonded, you basically buy a license in CA it has nothing to do with competence, the required bond is $1500 (I think), people use other peoples licenses all the time, and it’s not like he’s got the electricians license to run the electrical anyways. Not that a permit was even going to be pulled. We’re lucky we’re in a coastal zone and a Ca title 24 duct leakage test isn’t required.