Do supplies matter between Banner Saga volumes?

It has been a while since I played the Banner Saga 2 but from what I can remember, everything you mentioned carries over but there is a cap for supplies, the max supplies is 500.

Low level characters will be auto-leveled but the auto-level stats are terrible so I'd advise you to level them up now and max out any stats you feel are important (Break?).

Otherwise, if you don't level them up, since the characters get auto-leveled, you can save the renown from BS1 and use it in BS2 but as I said above, the leveling templates are terrible so you can test it out for yourself.

Also promotions cost less universally, items top out at 20 renown for a level 10 item instead of 25 for a level 5. So save all the renown you can. Clansmen are also useful in BS2 instead of a drag on your resources, carrying them over is good.