These are similar, but try one like
this or
this.
Note the comment on keeping salt out of the rub and salting first, separately. Since we're talking butt, see
this as well. It is a vinegar sauce I use with some things but not the comment [in brackets] on using it as a finishing sauce for pulled pork. I use it this way all the time.
On foil: Yes, correct, it is used for a braising or steaming effect, depending on whether one adds anything to the foil. If one adds something flavorful (I use a juice blend--usually pimeapple mixed with concentrated tamarind--for ribs) then it can adda flavor layer. I foil brisket but do not add anything to the foil; other cooks sometimes do.
Foil also has 'side effects' which, truth be told, are sometimes the primary reasons for its use: it speeds cooking, and it protects the meat from direct heat. In the first case, foil can be used well into a cook if time seems to be running out or it can be a planned thing and used to cut the overall cooktime; for the latter, many meats cooked at high heats. (I and others cook briskets ~325, foil after ~2.5 hours into the cook, then cook till tender, often at even higher temps.) High heat cooking forces a lot of evaporation and speeds rendering. This can be just fine for a while, but to facilitate evenness of cooking (higher heat cooking tends to be uneven) and to retain more moisture and rendering, foil works wonders. (Though I also cook ribs at high heat I don't always foil. For ribs it is more of a flavor layer thing for me, as noted. Though the heat is high, ribs aren't that thick--unlike brisket--and one can cook at high heat without foil.)
Because foil speeds cooking 'done' will be achieved sooner, regardless of whether one is low/slowing or cooking at high heat. This needs to be remembered.
I don't foil butts but some people do. Some do it only to speed the cook if necessary, and others always do it because they prefer the results.
Very large items like chuck rolls are usually foiled (often when the internals hit the 160s) so as to speed the cook
and to protect the outer portions of the roast. These are very long cooks and multiple hours of heat can eventually dry the surface irreparably, mostly due to the grainy nature of chuck. Though shoulders as well, pork butt (or whole shoulder) doesn't really require foiling per se, but it can be helpful to even out cooking and to make the cook shorter. I'd rather separate the arm from the butt but if you'd prefer going whole, have foil available and consdider it as an option if you wish. For pork shoulder I wouldn't bother foiling till the first plateau was broken, say ~170 internal.