Rain or shine water on front & rear floor of '98 Sunfire convertible; seats & interior dry. Removed heater core but water still there. AC needs charging so not using it.

classiic HVAC failure? LHD left hand drive car , no country told.
own for how long, 2years or 1day/ or what ( right passenger door?) for rain. ingress.
you said water, well that can be clean pure water
from RAIN or HVAC evap condensate,
using AC cool or heat + defrost mode? or just pure heat mode?
I do not know what you do there
i tray to capture water,in jar,and see if it is green or yellow or pink
that is AF antifreeze,
and put my fingers in it and rub fingers to thumb and it feels very very slippery, that is AF. not water
if i sniff it and smells sweet it is AF>
(3 ways to discover AF antifreeze)
ok it's water, so dont use AC or Defrost mode.
so that be RAIN or defrost condensart
sorry i could never even guess the water gravity effects from any car made from fire wall to rear of care, gee hills even change that.
learn to do deeper inspection of all carpets there.

bad door gasket
or last drove car with say a bandanna hanging out the door.
a 1 time event,nobody can guess ever.
and allowed rain to go inside any car.
or windows were not fully up.

if raining 100% normal. (rag top or hard top,?)
if the HVAC condensate drain PORT under car leaks pure water again 100 % normal. on AC or defrost modes, just like a beer can is wet .
same physics,(condensation)

if water is not water but is Green Coolant that is engine leaks.hoses, or RAD or over filled recover bottle. or
top of engine V gasket front ;rear leaks or coolant pump.
bad thermostat housing leaks too or wrong inside it gasket.
or heater core to right passenger floor well, core is bad.
my 08 jeep (rag) has no body drains for rag rain failures.
but the front cowl vents do. (so as not to food out HVAC air induction ports)
but not told what water means to you?
rain
condensate.
or engine coolant.

doors leaking rain water is huge topic, (seals)

sounds like your ac drain is plugged up and condensate from evaporator core is leaking inside

It could be the heater core. Usually it leaks on the passenger side, but it could be running down to the driver side. With you stating it has overheating issues, that's why I think the heater core. If this is the case, usually the whole dash will have to come out.

I have a 1997 Toyota Camry. Water was collecting on the front PASSENGER floor after a rain. I opened my sunroof and found the front drainage holes (about 1/8" diameter) in the corners of the track sunroof track. They looked clear. I poured a bottle of water in track and watched the result. Sure enough, water started dripping from the right ride of the glove box on to the floor. I started tearing out the interior panels to trace the leak. What I found is that if I poured the bottle of water REALLY slow into the sunroof hole = no leaks. But if I pour it too fast the small 1/8" hole cannot keep up and the track overflows! THAT is where the leak comes from in my car! If water overflows the track, then it makes its way down the column trim, around the glove box and on to the floor.

So I need to help the 1/8" sunroof hole drain faster. I took some 18AWG TFFN electrical wire and jammed it into the hole to help clean it out. I then removed the black plastic mud flap behind my front tire and blew out all of the leaves and rotted debris that where behind that flap. It was packed with junk! I poured more into the 1/8" hole and it seemed to drain quicker.

I hope this information helps others.

The evaporator drain is plugged with debris and filling up the heater case. Remove the 90 degree elbow and clear the drain hole at the case.(pencil or piece of wire) You will know that's it when it dumps out a half gallon on the floor. Be sure to reinstall the elbow to keep out rain/ road spray.

check valance drains
they ar likely pluged or disconected

Yes, your heater core is leaking. Dash will likely have to come off. Along with everything that is tied into the dash. Best thing to do is to take it to a repair shop. But before you go off to the shop.. take up the carpet coming from your passenger side front..just pull it back. Far as it will go. Then get the car hot. Run your heater full blast. Also place a white rag at the vent under the passenger seat. It maybe leaking into the ducking and flowing out through there. GOOD LUCK!
Here is a link to how to change the heater core yourself...IF you have the proper tools. As it does require you to evacuate the freon...evacuating into the air is ILLEGAL and there is a very very hefty fine for being caught. $10,000 fine I think

sounds like you have a window seal leak.  The only other way water will leak into the car is a leaky heater core or a clogged A/C drain.  Do you have a sun roof that could be leaking?  As they have drains too. 

If Your Fan is operating properly, along with Your defroster Meaning Your A.C. Pump is charged and engaging, I would have to take a look at Your heater-core to see if it may be leaking on to Your floor on the passenger side. Therefore causing more moisture in the car than can be evaperated under normal conditions... Hope this may Help!