Before someone says RTFM, let me just say..

I DID!

Okay, Just so I know the status of everything, I want to go ahead and change
the oil in the trans, and the rear end on my recently purchased 97 M model.

From what I have read, I assume, being an M it has the Torsen LSD rear end,
although I can't find any concrete verification of that fact.

The manual simply says GL5 gear lube for the diff, and the trans.  In every
other car I've had with any type of LSD, I had to add a friction modifier.
Is this necessary for the Miata ?

I'm also planning on running synthetic gear lube in both.  Is there any
reason I shouldn't  do so ?

The car has had Mobil1 in the engine as far back as the records go, so I'm
going to continue that as well.   Although I'm not typically a synthetic
proponent, it seems to make sense for a small, hi-revving engine.  Also,
since that's what it has been fed, I'll continue.

What brand of oil filter is good to use though ?  (I know enough to stay
away from Fram), but I always used a Motorcraft filter in my other vehicles.
Is an OEM filter the way to go ?

Oh, BTW I did also scan the garage section of Miata.net for these questions,
and wasn't able to find answers.

Thanks, all!