Is the 82nd airborne training in conducting amphibious landings with their LAV's they acquired from the USMC?

I seriously doubt it. Amphibious landings aren't a part of the Airborne doctrine, the amount of LAVs is too small to support any kind of landing, and the 82nd has no beach craft to deliver equipment for an amphibious landing. They got the LAVs because they're light enough to drop without shattering apart.

They needed something "heavy" to drop and the Stryker is far from being air droppable or even C-130 transportable. Instead of using M113s or bringing back the Sheridan, they just got the LAVs.

There are situations where a potential mission in planning will require equipment specific vehicle training in the event a political decision is made to execute. The senerio may be the use of equipment already on the objective that was purchased by the threat. Back in my day, we were required to conduct training on a light armored vehicles (M551) of a potential threat which there was the possibility of deployment. It never happened but we were prepared to opreate available equipment as an operational enhancement. Airborne does arrive by air but on the ground, it is light infantry that will take advantage of the threat's equipment that was an operational contiguency. Things change, no one can predict what resourses a unit will utilize during the Fog of Battle.