I don't know which year truck you have or the radio/system options you have, so it's hard for me to answer your questions. However, I don't believe the stock Rover amp has very much power. Additionally, you would probably not have the ability to adjust the power to the sub to balance the system. And finally, I'm not sure if the stock Rover amp even has a low-pass channel.
Will it work? Sure. But one thing I'd look into is the low-pass feature. If the stock amp does not offer this you may want to find an aftermarket low-pass filter to mount in-line. This will rob some power from the already underpowered amp. If you do not have a low-pass filter somewhere you risk burning out the voice coils on your brand new sub. Personally I would not try to use the stock amp. Amps are cheap these days.
It's been so long that I cannot answer your depth question. I know the Pioneer sub I installed was a tight fit. You could probably make a 3-7/16' sub work, you just may need to make some fort of spacer, maybe, to lift the sub a tad. Not sure.
Don't skimp on the dynomat. You need it. No question about it. The LR3 tailgate is seamed at the bottom. This is probably to allow any water or moisture to get out. I don't know. So I would not caulk or otherwise seal off the bottom of the tailgate. But you need something to deaden the thump. If you don't do this your system may sound decent inside the truck, but it's going to sound like a joke on the outside. You may also need to pad the backside of your license plate so it does not rattle.
4ohms is standard for car audio. Depending on the amp you get you may be able to divide the ohms for more power, but uncalled for in this application. Don't read too much into that.
Will it work? Sure. But one thing I'd look into is the low-pass feature. If the stock amp does not offer this you may want to find an aftermarket low-pass filter to mount in-line. This will rob some power from the already underpowered amp. If you do not have a low-pass filter somewhere you risk burning out the voice coils on your brand new sub. Personally I would not try to use the stock amp. Amps are cheap these days.
It's been so long that I cannot answer your depth question. I know the Pioneer sub I installed was a tight fit. You could probably make a 3-7/16' sub work, you just may need to make some fort of spacer, maybe, to lift the sub a tad. Not sure.
Don't skimp on the dynomat. You need it. No question about it. The LR3 tailgate is seamed at the bottom. This is probably to allow any water or moisture to get out. I don't know. So I would not caulk or otherwise seal off the bottom of the tailgate. But you need something to deaden the thump. If you don't do this your system may sound decent inside the truck, but it's going to sound like a joke on the outside. You may also need to pad the backside of your license plate so it does not rattle.
4ohms is standard for car audio. Depending on the amp you get you may be able to divide the ohms for more power, but uncalled for in this application. Don't read too much into that.