jdtsmith,
Your call on what size of a joist to use. When I build a deck (I'm a deck contractor), I use 2X6 PT joists and install an additional beam due to the reduced span. (My choices of PT joist mat'l is 2X6, 2X8, or 2X12 -- 2X10 would be a special order and would cost about 40% more than a 2X12.) And
ALL of my framing is done with ACQ PT -- posts, beams, and joists.
As far as the post to beam connection, Simpson makes BC's for using a 4X4 post to support a double 2X beam -- BCS2-2/4. You are probably on the right coast and can't get a 4X whatever for your beams, so a dbl 2X is what it is. Your beam is in place -- lay the joists on top of it.
What you are showing in your drawings is the simplest way to frme the steps. Use LU hangers (LSSU210's) to support the stringers that are perpendicular to the facias that are square and LSSU210-2 hangers for the ones that occur at the 45 degree corners. Get a Simpson catalog!! (
Simpson Strong-Tie - Helping to Build Stronger, Safer Structures or 1-800-999-5099) It'll show you everything that you'll need.