Double rim joists on deck

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...

The rule, at least here in the US, is a cantilever can extend no more than 1/3 the supported length (so, you could go ~3 feet further). Personally, I try to keep cantilevers no more than 2 feet, regardless of total supported length: while it might be OK structurally, it will likely sag the further you go, and can feel bouncy.

To do the best job, get some 12 foot 2x8s and sister them with the existing joists (run them the entire length, nailing with galvanized nails at the top and bottom every 16 inches). Then put a double joist hanger at the ledger against the house.

One of the critical things with a deck cantilever is how you attach the railing posts at the end of the cantilever. You will be nailing a 2x8 rim joist at the end to finish the deck, but you need to make sure the posts for your railing are tied in securely to the joists, and not just the rim joist. The method can vary depending on whether your existing railing posts are notched into the decking or fastened to the outside of the deck.