[Attilathecanuk]

First get some ACQ treated 3” screws and secure th ledger to the house with same pattern as those nails (PWF lumber will corrode those nails). A 3-ply 2x10 beam will support your joists and I would use 2x10 for joists as well with one row of mid- length bridging or blocking. I would do 3 posts (screwpiles) under that beam 2 feet back from the edge of deck (or 10 feet from the bump out of the house).