The MAP sensor doesn't do anything important. you can try cleaning the connectors on that one and see what happens. It's just behind the windshield washer fluid jug.

The symptons are consistent with a bad air pump: hard cold starting, cooling fan that runs when the engine is not hot, and running a little rich.
No, those are a bad ECT (coolant temp) sensor.

The air pump doesn't do anything either to affect the running of the car. Do you hear a whining at all after you put the car in gear, drive around for a bit, and stop? Often times the air pumps are killed by moisture getting down into the system (my car has had 4 in its history before I owned it)...Klaus here recommends drilling holes in the housing to let the water drain out. If you need to pass emissions testing, this will need to be fixed, otherwise it's not important. I kept clearing my code for months before it finally got on my nerves enough to fix. It is expensive, there is a write-up over on MVS for retrofitting a VW air pump to a Volvo and save yourself quite a bit of money.

I'd start by replacing the ECT sensor and thermostat. You can pick up a MAP sensor at a junkyard - they are very expensive new.