No, they are not reset after each flight, but as commented, the FDR and CVR are on a loop, and just keep recording over the old data. For US registered aircraft, FAA Regulation "14 CFR 91.609" covers flight data recorders and cockpit voice recorders.
It states for flight data recorders:
(c) 1. No person may operate a U.S. civil registered, multiengine, turbine-powered airplane or rotorcraft having a passenger seating configuration... of 10 or more that has been manufactured after October 11, 1991, unless it is equipped with one or more approved flight recorders that .... are capable of retaining no less than 8 hours of aircraft operation.
(c) 3. All airplanes and rotorcraft subject to (the above)... manufactured on or after April 7, 2010, must ... retain at least the last 25 hours of recorded information...
For cockpit voice recorders:
(h) 2. All airplanes required by this section to have a cockpit voice recorder and a flight data recorder, that are manufactured before April 7, 2010, must by April 7, 2012, have a cockpit voice recorder that also ... retains at least the last 2 hours of recorded information ...
There are not "thousands" of parameters.
The CVR must record the following 25.1457 (Cockpit voice recorders):
(1) Voice communications transmitted from or received in the airplane by radio.
(2) Voice communications of flight crewmembers on the flight deck.
(3) Voice communications of flight crewmembers on the flight deck, using the airplane's interphone system.
(4) Voice or audio signals identifying navigation or approach aids introduced into a headset or speaker.
(5) Voice communications of flight crewmembers using the passenger loudspeaker system
(6) all datalink communications
So, probably 6 or so channels.
For the FDR, wikipedia states "There are 88 parameters required as a minimum under current US federal regulations (only 29 were required until 2002), but some systems monitor many more variables."
So, if the flight lasts less than two hours, there will be at least the whole flight on the CVR. But if the flight is longer than two hours, you only have the last two hours.