Second level spells are: Continual Light, Detect Evil, Detect Invisible, ESP, Invisibility, Knock, Levitate, Locate Object, Mirror Image, Phantasmal Force, Web, and Wizard Lock. Let me know if you need spell descriptions.
He thanks you for the briefing and will check about his "double". He says the cat is his familiar.
There's a temple in town and a jeweler/banker-type building.
The Blacksmith will let you trade one of the suits of human plate for dwarf-sized plate.
There's not really an armor slot for helms, it's kinda part of the armor if you want it.
You have to buy regular arrows by the quiver, so I'll just say you bought a new quiver plus the silver-tipped arrows.
There's nothing like a silver-inlaid axe available but the blacksmith can make it for 500 gp. It'll take half a week (again, doesn't really matter since we're between adventures).