I’ll start this off, but i’ve got plans for the next week so i won’t be able to go into a lot of detail on everything you listed. Other Community members please help out.
As in the EU, the USA has numerous significantly different culinary regions and it’s the same with BBQ. You will have to try a few recipes to discover what you best enjoy as there is rarely a common standard. I feel like saying, - There’s no bad BBQ. And that’s almost correct. I’d add, - . . . except in American BBQ restaurants. Chain restaurants in particular frequently take shortcuts and mix regional techniques and flavours resulting in culinary junk.
Also, a lot of people confuse grilling with BBQ. They are nowhere near the same cooking techniques.
Pulled Pork: - see Ember’s US chart. You picked the correct Spanish cut.
The butt is the most often cut used, it’s up to 8 pounds (3.5 kg.), and sometimes the whole shoulder is used, about 17 pounds (8 kg ), but i would avoid it. The shoulder is just too big for home use and takes too long to cook well.
I select pork butts by examining the muscle end, opposite the bone end. The muscle should feel firm and have ample fat marbling. That’s what makes for a great butt for slicing or pulling.
Pulled Beef, - never done it, never needed to, when Pulled Pork is so delicious.
Pulled chicken; - just whack-up a whole boned cooked chicken.
Pork Belly; use a pork belly, either bone-in or boneless.
Brisket; - Beef Brisket, probably the most difficult cut of beef to cook really well. A whole one weighs about 8 kg. It consists of two pieces, the Point and the Flat separated by a layer of fat. Many newcomers to BBQ start with brisket and are disappointed by their results wasting a lot of money. If you are going to BBQ one, start small.
The best way to learn is to find a Texan and cook one with her/him. There’s a lot of tricks to it.
I thought this was a Sous Vide Community.
Corned Beef, usually cuts off the Brisket, either the whole Point or Flat or parts of them. Corning is salt curing. Spice it up and call it Pastrami.
Sometimes Corned Beef is made using the Shoulder Clod and the Eye of the Round.
Beef Roast, not a usual BBQ item that i am aware of, but i will do a smoked and slow-roasted rib eye . More often done in South America. You can BBQ just about any cut of meat once you have mastered the most common techniques.
I am surprised, and relieved, because you didn’t have on your list the most frequently cooked BBQ menu item in America, Pork Ribs.
Thank you, because i’d probably have to take off my shoes to correctly enumerate all the various rib cuts and preparation techniques.