I use carpeting underlayiment. but be aware if you live in an area with a lot of rain/salt it can get wet. An alternative would be rubber mat that you can get at stores like Tractor supply by the foot. It's ~1/4" thick and should prived some level of dampening.
Door panel removal is pretty much the same Get a tool! You can get then at any parts store...
Even WalMart has them. You can "feel" around for the points that are secure, insert the tool (carefully) and pry out the clips quite easily. Or, a firm grasp and pull will also loosen the panel.
There are also screws: one in the door handle, maybe two at the rear of the panel, and 2-3 along the bottom of the panel. Use a GOOD screwdriver; amazingly, the ones (also at) Tractor Supply for $1.99 are amazingly good! There are also screws hidden under the trim panels (door grab, etc) but someone else would have to tell you exactly. These may be large screws, so a bigger driver is in order to avoid damaging the heads.
When pulling, don't forget wires!! Window switches, mirror wires etc are often tied to the panel, so go carefully and look for connectors.
BTW, now would be a very good time to upgrade the speakers...