Coolant leak 2002 elantra leaking coolant heavily, but not all the time, no visible cracks or leaks will run ok then out of nowhere start to pour out from front passenger side

possible cracked overflow tank--disconnected or damaged hose

You could have a cracked radiator hose that is getting ready to burst or a cracked radiator that leaks with pressure.

Did you check the front floor board,heater core could be leaking?

the test is easy
it uses the magic of the system has 12 to 14PSI pressure all the time.
hot. so park it get it hot. to 180F (old thermostats fail, they are #1 failure ,so why would you discount that?????)
ok its really hot , my pryo gun shows 180F ,ok real hot is true. no bs.
so now look for leaks.
if you see none
and the passenger toes are dry (heater core drips)
then there are on external leaks,
if true that, then its INTERNAL LEAKS!

head gasket is failing or the A/T or engine oil pan is full of AF.
are you running 50%^ AF all the time, ?????

everywhere you drive do you look after parking, for ground leaks.?
as you leave car and when you come back.
you must. or miss the boat.

Your heater core is leaking.

This does sound like your water pump is leaking, or your head gasket has busted on the outside edge. I would check the water pump first, as it is fairly common for the seal to bust and leak coolant from the water pump.

I’m happy to help further over the phone at https://www.6ya.com/expert/jeremy_69f3cc28d95bf514

some 3.0 engines hive a head gasket leak on the rear head on the corner hear the water pump..

could be a hose leak or radiator leak, get fixed asap could overheat engine.

Sounds like you have a faulty head gasket or maybe a cracked head.This can cause overheating and the check engine light to come on.The code for the o2 sensor is probably caused by coolant getting into the exhaust system and coating the sensor.The coolant fan may work but it cannot remove enough heat from the rad to make the engine cool off.Try some engine coolant stop leak to see if it will help.This maybe only a temperary fix.Let me know if you need more.MOE

check coolant level,check rad for leaks,hoses,water pump.