Yes. The acute phase of healing is usually over after about a week, but the bone under the gum tissues continues to heal over the next several months.
Depends on type. So much in dental treatment depends on the patient, their pain tolerance as well as the type of extraction, ie; bony, or ankylosed. A surgeon's skill, touch & the way they do a surgery. Great hands with a patient who follows all of the home care directions can lead to a very positive result with very little pain. With all the variables, pain could be minimal or could last weeks. Meds can help.
Feeling better in wk. It will actually take months for the sockets in the bone to heal, but discomfort should be well on its way down after 3-4 days unless you develop a dry socket. The gums should feel a lot better after about a week. It really depends on the amount of trauma that was incurred by your mouth.