That'd be the fairing, the 'nosecone' that covers the payload during launch. It wasn't shown in the webcast because it has a low probability of success (they've made several attempts so far with varying degrees of accuracy and damage) and because there's no live feed from the fairing as it descends.
The aim is to get it to land in a predetermined spot in the ocean with steerable parafoils, then eventually to stick a 'bouncy castle' at that spot to soften the landing.
Yep — Pathfinder and the Mars Exploration Rovers (Spirit & Opportunity) both used airbags. NASA has since switched to the 'sky crane' method for Curiosity and the fortcoming Mars 2020 rover, lowering higher-mass payloads to the ground without contaminating the surface with rocket exhaust (as with Phoenix and the Vikings).
People speculated that SpaceX might do something interesting with the second stage, but it's just speculation. The last time it was rumored something interesting was done with the second stage -- a test of longer-duration operations on the NROL-76 mission -- nothing was said before or after.
This was apparently a very light payload, so there was lots of room for experimentation - attempts at recovering the fairings, and further speculation at playing with the second stage, and just playing with tolerances and approach angles given sunk cost of the extra launch power. Us fans don't always get to see or hear about those early experiments though.
They've been working on fairing recovery for some time but they likely won't provide coverage until they've got all the parts sorted and can do it successfully.
