Yes, Gravity Drive and Flank Speed also work, as they work on all ships in a fleet. Any tech/ability that works on all types of ships will work on Flagships. But techs that only work on specific ships (like Type IV Drive) do not affect the Flagship.
Re: Promissory Notes, keep in mind that if playing rules-as-written, you cannot just arbitrarily trade or give away Promissory Notes - you only do so during the Political Card phase of either the Political or Assembly strategy card. Some have house ruled, however, that you can exchange them anytime you want for any reason.
As for #3, the defender chooses the order. Note that when you choose an effect, both sides resolve that effect simultaneously, though, if applicable. For instance, if you choose to resolve Assault Cannons, both sides with it use it together, you can't say "I'm using Assault Cannons, you'll use yours later".
Also, just remember that PDS fire is not considered a pre-combat effect. It happens as a separate step and thus PDS fire always occurs before everything else (and you can't use Direct Hit with PDS fire).