Select A/C and hot air, maybe compressor is not kicking on due to low freon in system, maybe, or loss of battery power to compressor/A/C system, however, blower works, so that's good. I suspect low gas in A/C. Look for a leak with leak detectant.
Low temps while cruising, thermostat is stuck open. If you open the coolant system, might as well re-hose it, flush the block, clean the radiator, if not replace it, re-belt it, and new coolant, 50/50 mix. Be sure to purge the air out, may take several overnight cooldowns to accomplish. Make sure reservior is clean and no leaks, replace radiator cap.
Oil between injectors could be coming from center intake bolts as they go into crankcase. PVC valve and hose and nipple may be plugged or not working. Also, could be too much blowby from worn rings, excessive crankcase pressure shoving out oil through bolt threads. Or, leaky valve cover gaskets.
High idle when cold is good. White smoke at startup means vlave stem seals are worn, heads may need reworking, for a later time.
Fans not working could be one side of fan relay not having battery power due to blown fusible link at starter solenoid post, or blown fuse. The one fan being on when A/C is not selected and turning off when A/C is selected means one side of relay coil has no battery voltage. The other wire of the relay coil is the control line from PCM. When PCM calls for fan relay to energize, the PCM control line goes low. If coil has battery voltage on the other coil wire, relay energizes and fan comes on. But, just opposite is happening, so no battery power to one side of relay coil.
The other fan not coming on could be due to a broken thermo switch, either on the pass head, or next to the thermostat housing. Or once again, no battery power to one side of relay coil.
Get a Haynes manual for the car model and read up. Take it to bed and through osmosis, the info will drain right into the brain......LOL.
Lemon? You pay for what you get.....a used car.