Another n00b question for you BA veterans, hope you don't mind...

A friend and I have four legs booked in AA Domestic First Class (P Fare Code). He is BA Gold and I am currently BA Blue.

Flights are as follows -

ATL - DFW
DFW - LAS
LAS - DFW - ATL (no stop over in DFW)

Am I correct in saying this would count as four segments or would the LAS - DFW - ATL count as a single segment? If it counts as four segments would I be correct in assuming this will net me 240 tier points (60 per segment)?

I only need a few more tier points to bump me over the Silver threshold...

I have already tagged both of our BAEC accounts to the booking with AA, so will (or perhaps I would be better to say should? ) the tier points and miles automatically post to our accounts or will it be a case of claiming the missing miles etc. once we have flown?

What does the P Fare Code actually mean? I read somewhere that this is used to signify full fare First Class on a three class flight? Does this mean there will be Coach, Business and First on these flights? Flying AA Domestic what is the actual difference between Business and First?

I have never flown AA Domestic First Class before, but have flown both Club Europe as well as UK Domestic. I read in another thread posted here recently that it is a 'sort of' mix between the two.

Thanks for your time!