I feel for you, any inspector should have noticed these things the instant they stepped in the house. You local code may differ, but kitchens do need a vent above the range, whether it be directly vented to the outside or the cheap recirculating ones. Venting directly to the outside is really the only way to go, venting directly to the attic is not only not allowed but could be dangerous. All stoves need to be vented, whether gas, electric, you name it.
For insulating the ducts there are two methods, you can either wrap it with special duct insulation or slide on sleeve insulation. Since it's installed you'll probably need to wrap it, taking care to seal all the joints with the proper tape (not duct tape). Insulating the other areas of the attic, I'd just match what they placed elsewhere, so if fiberglass batts do the same, unless of course they didn't use enough, so maybe it's a complete reinstall.