There should still be trade fleets that spawn, consisting of primarily freighters.
The only way to get a capital ship, other than defeating a fleet and capturing one, is to become cooperative with a faction and purchasing one from the regional capital (Vella for UIN, Khabara for XLE, Vostok for RSF, Danbridge for ISA). There's no wiki for Ironclads, but the Codex ingame is not bad, combined with the Starsector wiki for the general mechanics of Starsector.
It looks like the Flag items are still in the code, but aren't dropped or have the ability to be sold to another faction anymore.
The different pirates spawn in the Midline system (Marauders) and Pax system (Black Widows Raiders). Marauder fleets fly over to debris heavy areas (such as the Grant system) and salvage things for days, and then return home with ship parts and such. The Black Widows fly around, and end up with Luxury Goods, Recreational Drugs, etc if they raid and survive long enough, then return home. Marauders generally feature a larger focus on missiles, in general their ships are crappy, but are nasty offensively. Black Widows focus on energy weapons, although they pack a number of the ISA's Barracuda LRMs and use them when you get close to overloading.