The drian plug for the AC Evaporator is either not installed properly or clogged. If the AC was not worked on recently get under the car, find the drain plug and clear the drain out (With a straw or pen) Do not use lots of force. In most cases you can take the car to a place like Tire Kingdom of Goodyear and they will just shoot up a little compressed air up the drain plug. This usually clears up the obstruction. If that doesn't work you will have to do some work on the evaporator housing
It sounds like you may have a bad heater coil. Next time you get a puddle, smell it... Chances are it is coolant and not water
water in passenger floorboard, where is the hose that would cause this?
A damaged heater core will cause coolant or water to leak onto the passenger floorboard.
Leak in heater core
passenger side floorboard on the firewall close to the kick panel
Does it smell like antifreeze? If so, it is most likely a bad heater core, or one of the hoses feeding it.
ac drain stoped up or heater core bad
There is no drain plug but a condensation drain tube located on the passenger side firewall or just below ( rubber tube sticking out ) It may be plugged and a coat hanger or compressed air will open it. Your heater core may also be leaking if there is also coolant on the floorboard. If so it will need to be replaced.
There are many things that can cause vibrations in a 2000 Toyota Avalon. One such cause could be a bent rim and another cause for the vibrations underneath the floorboard is the engine.
heater core
Water.
Sounds like a heater core is leaking. That is a very common problem. You will be far better off to have both the heater core and the AC evap replaced at the same time. they are both in the dash and they both commonly go bad. fix both with the same labor.