Water leaks onto the passenger floorboard during heavy rain

You need to find the conduits for rain - one of them has a leak in it probably from corrosion. Try to locate just where the water is getting in and see if you can use a sealer to stop the water from getting in.

I would remove the glove box and anything else in the way and look for the source when hosing down the car.

If it has A/C the drain hose could be blocked and if no A/C it could be a leaking windscreen seal.

it is leaking from the outside air intake there is a hold there to clean it on on the passenger side top grill by windshield ask me more will explain

would it be the heater core leaking

I had the exact same problem with my 1995 neon. It was leaking around the tail light. I pulled the tail lights off and put a heavy coat of RTV silicone on the gasket, and 2 years later never happened again

My guess is the window seal.

Look for moisture on the glass of the windshield, as well as the passenger side door, if thebottom seal isnt making contact on the door glass water will run in threw the door

There is a leak from your cowl area.There is a technical service bulletin to install a plastic extension onto the cowl cover so water will not leak in side. It will also damage your blower motor if you don't get it reapred.

You could have a leaking windshield seal, and its running down the inside of the dash and onto the mat. Has the windshield been replaced?

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.