They don't know their world boundaries. Arya is goisng to see what's west, jon is either
-escorting wildlings to the place they choose to settle and check it's safe now, then come back to night watch. It's, of course, expected to be safe now that night's king has been defeated but, who knows ? They don't know th northern boundary, there could be a night kings hive there ?
-on his way to explore north up to the pole and beyond (assuming their world is spheric)
-establshing himself as king of wildlings (i don't think he his, tbh.His red head pal seems qualified)
Bran let her secede because ´
-North always had a large autonomy, and gave much blood to defeat cersei
-he knows she wants to be queen, and doesn't want to marry her, so it's the easiest way.
-nobody wants a war against north,no one feels comfortable about imposing something to sansa, and everyone knows how stubborn she can be.
Sansa won't pardon jon because:
-she has no right to do so in the name of whole westeros, she cando it in north's name only.
-she's happy having her own kingdom and doesn't want any opposition to use jon as an excuse to decrown her.