*gives old-fashioned look*

It sounds like someone has replaced the rusty floor without actually cutting the old one out, so you've got a sandwich. Not a good idea to be honest. Did the car come with an MOT? Sounds like a bit of creative panelwork to me...
If the carpet gets wet when the engine is running (and the wetness is warm) then it's quite possible that the heater hoses have perished and you're losing hot coolant in the cabin. If that is the case, then they need replacing - obviously the engine needs its coolant in the radiator, and not forming puddles by your feet - it will do no good there at all! Replacement of those is fairly easy, however.
If you're 5'5", it may help if you put some blocks of wood under the rear legs of the seat - it makes it swivel upwards, so the seat is higher, a little flatter, and it makes it easier to reach the pedals. You also get a view of the road that is (slight exaggeration alert) rivalled only by 4x4s!
Take the carpet out of the front, and any damp sound deadening also - you may need to remove the four bolts holding the seat in to do this. Then, you should see the holes for the bolts - one set may well be a little further forward than the set that were used - try and refit the seat using these. The unused holes may be filled with sealant (although I doubt it) so you might need a thin srewdriver, or a nail, to bodge through the hole and clear the debris.
Good luck - you'll get it sorted, and hopefully without cutting extra holes in the adjuster! ;)