To exit the sewers, you'll need to locate an orange (red?) flag on the map. The sewers in particular won't let you come back out from the entrance, and can get quite convoluted and tricky with its layout. I recommend just exiting every time you exit because it's easy to get lost and struggle to find the way back if you try to explore the full map, and the sewers reset as soon as you leave, so you can dive straight back in if you want. Loot doesn't have a delayed respawn like the cave in the park does, and it's mostly more efficient to just do things that way.
I've only found a few basic single item recipes (single meat, single vegetable, single fruit, single fish, etc) through trial and error apart from the apple pie recipe you can learn through Arane's quests. Might not be ready yet but I'm sure the dev can clarify if I am wrong. Can't say I know of other crafting options outside of the three books you can find at home/college/in the forest either.
Professions will depend on the profession. There's only one tailoring recipe and I have no idea how to get sheep to produce wool right now (or if that's not quite implemented yet since I can't seem to find proper sheep feed either), but spiders in the sewer sometimes drop wool, so I've actually gained some tailoring exp that way. Mining is super easy, fishing just requires you to fish in the lake (and while you can buy a rod, I'd wait since I remember somehow getting a rod during Nekuro's later quests - it'll just save a bit of money in the long run), lockpicking requires you to actually pick locks in places like the sewers (and without any clear means of crafting lockpicks, you need to get them from chests, so it's very easy to end up in short supply - never sell lockpicks, you'll regret it later). Business administration only comes from buying/obtaining businesses, but there's only two I am aware you can buy at the moment and that only gets you to 70 total points, so I'm sure there's still more in the works there too (and if you want to try this but the amounts of money seem way too much, trying getting the shop owner to soulmate and inquire again - it's worth the effort, imo)
That's... probably too much all at once, but if you have a more particular question I might try to answer it still.