2x6 deck joists: salvageable or need replacing?
According to the table in the 2012 IRC code a exterior deck needs to handle a 60lb per sq ft (40 lb live + 20lb dead load). Most treated lumber that I am aware of is #2 southern yellow pine, using that criteria on the table in the code book, your joists can carry a 10'-9" span.

The biggest failure in deck construction has not been the posts or the joists, but the connection to the house. I believe code now requires through bolts into the band joist, or the joist of the house, or posts at the house is cool too.

The length of the post will dictate whether they need to be 4X4 or 4X6. Its a deflection (bowing) thing. IMO 4X4 for a 10' span is not overloading the post, a 16' span may...