It's best to take the cover off.  That way you can get a look inside, and
check things out.  You'll need some RTV to re-seal it.

Sure - though it might be better to use a catch pan with an open top - the
gear oil's going to dump out pretty much all at once, and the drain pans
that just have the center drain hole might not drain quickly enough to
prevent the gear oil from overflowing.  Depending on clearance, you may also
want to drop the spare tire.

A gasket scraper...  there'll be at least one spot where the flat part of
the carrier extends beyond the lip of the cover, where you can slide the
gasket scraper between the two.  A trick is to leave the top two bolts of
the cover in place, just loose (very loose) - that'll prevent the cover from
falling when you break the RTV seal.

Once drained, clean the cover and carrier mating surface with some brake
cleaner, and run a nice 1/8" bead of RTV around the perimeter of the cover,
going to the inside of the bolt holes.  Slap the cover back in place (try to
get it aligned the first time - don't want to be squishing the RTV back and
forth too much), and torque the bolts to 25 ft.lbs. in a criss-cross
pattern.  Let it set up a bit, then re-fill with gear oil, and friction
modifier if you have a limited slip.

I prefer a gasket, NAPA carrys one.  Remove the bolts-tap cover with
hammer. Clean it up & reassemble quick & easy job