Work the problem in order. Radiator fan first. Then see if it overheats using a thermometer. If it does, pull the thermostat and see if that gets it under control. Replace thermostat if needed.

If it runs hot without a thermostat, you may have a clogged radiator that needs boiling out or replacement.

Once you get it to where it doesn’t overheat on the thermometer, put the thermostat back in and watch while it runs for a while. It should come up to temp stamped on the thermostat and then level off.

Then put in a new coolant sensor, put the radiator cap on and rerun the coming up to temp and leveling off test using the dash gauge.

Next is serpentine belt. No real trick to that as long as it’s routed correctly.

Finally, clean the top of the engine and try to suss out where the oil’s coming from. Probably just a valve cover gasket, or maybe a bad oil fill cap or leaky PCV grommet.

Have fun with your new baby.