Are gum grafts, when healed, as tight around the tooth as "normal" gingiva attachment?

Generally no: But the tighter the better.

Yes: A properly-healed soft tissue graft will be a long-lasting, stable soft tissue attachment around teeth.

Yes, take 3 months: Gum graft heals in 2 weeks for attachment, then 28 days or 4 weeks for cross linking of tissue Amino Acid chain. However, it may take 3 months for reestablishment of all fibers around the tooth, when the sensitivity often subsided. Keep the area clean is the must.

Yes: Recession of the gums = bone loss. The root of your tooth should be covered by gums and bone. Attached tissue is needed to avoid further recession and bone loss. Gum grafts increase the attached tissue on a tooth. If healthy, the attachment is strong and prevents further bone loss. If not properly cleaned, the gums get inflamed and the attachment becomes weaker.