If the gutters are bent or corroded they can be taken down and reinstalled. If they're sagging hangers can be added to true them up.
Solar powered vents are a waste of money. It's good the peak vents are in place. Have the contractor make sure the screens on the inside aren't failing. Can let in bugs, bats and birds.
A membrane is used under the shingles along eaves. It's quite thick and has an adhesive on the back. It grabs nails and the joints seal. Makes it hard for water to get in under the shingles. Critical to protect against ice dams. Should extend two feet inside where the wall and roof intersect. After that tar paper is used.
Three tab shingles are the least expensive. The really cheap ones are quite thin. I prefer to use an inexpensive shangle. These have an extra layer of material, so they last longer and don't require careful vertical alignment, so they can be installed more quickly. They also add more visual interest to the roof.
The minimal nailing pattern for a standard 12" x 36" shingle is four nails. In high wind areas six are required.
Roofing nails MUST be galvanized. When they throw rust it's because a cheap nail was used and not sealed. Make sure any exposed nails have a dab of sealant over them.
One of the places roofers compete is on the quality of their warranty. READ it carefully. There's probably a statutory minimum, but check what the material warranty is and what the labor warranty is.
Remember : a contract is an agreement between two people. IF something isn't covered you can have it added. Same thing with something that advances the contractors rights over yours.