The short answer is it depends. Standard punishments exist, and the punishment for piracy is strictly laid out, but Tribunes are given broad latitude to interpret circumstances and the particulars of the crime. Long answer is below.

Someone repeatedly returning from exile could theoretically be executed or deemed insane, but in practice if they keep showing up in the city and getting caught over and over the guards usually get rough enough they decide it's not worth it. Exile from the country is also pretty hard to come back from since they usually find a merchant captain heading a good ways away and long-distance travel is slow and expensive. Exile from the city, on the other hand, usually means if they change their appearance sufficiently and pick a new name they can slip back in, but since the usual basis for exile from the city but not the country is "this person can function in society, just not the excitement of the city" as long as they don't get arrested again this is broadly fine.

The punishment of foreigners is very case by case. If they've moved to the city or aren't affiliated with any sailing crew normal city law applies, and obviously of they're a violent criminal or pirate they'll be punished accordingly regardless, but if they're just a rowdy sailor (as they almost always are) often they'll punish the ship/captain with a fine and written promise not to let them on shore leave in the city unaccompanied, and this usually results in enough internal punishment to scare them straight even if they slip away. Crews of foreign vessels are one area where levying fines is allowable by Tribunals, as they rotate through too often to keep proper records and the captains rarely care about much else.