Does Season 0 of the Pathfinder Society use 3.5 rules or PFRPG rules?
I assume it uses 3.5 rules since the product description says "...suitable for use with the 3.5 edition of the world’s most popular fantasy roleplaying game."
The Season 1 product description says "...suitable for use with the Pathfinder Roleplaying Game" so I assume this season uses the new PFRPG rules.
Will Season 0 ever be updated to incorporate the new PFRPG rules?
The Season 0 scenarios are to be played with PRPG characters (per the Guide to Pathfinder Society Organized Play) even though they were originally written for 3.5. Since PRPG is backward compatible with 3.5, a GM running a Season 0 scenario under PRPG should not have to make more than a few adjustments (such as calculating CMB/CMD) and is expected to run the scenario under the PRPG rules set.
You can also find the answer to many of your questions by reading the rules for Pathfinder Society: the Guide to Pathfinder Society Organized Play (which is a free download).
Will Season 0 ever be updated to incorporate the new PFRPG rules?
As for this: no. I'd rather focus on moving the Society forward than spending time re-writing and converting 3.5 scenarios to PRPG. Besides, since 3.5 and PRPG are compatible, it's not that hard at all to run PRPG characters and rules through a 3.5 scenario.