Depends. Knee arthroscopy is highly dependent on the procedure being performed along with it. Trimming a torn meniscus can lead to immediate relief and return to function while acl or PCL reconstructions take 8-9 months to recover. It also depends on your conditioning before surgery. Pain from quad weakness and tendinitis will not improve at all after surgery. It will depend more on rehab.
Varies by procedure. If it is for a meniscus tear, most people are moderately sore for 3-5 days. Swelling improves starting around day 4 or so. Most people take pain meds for 2-10 days. Some take no narcotics at all. Crutches for a day or two then sometimes a cane. Most are done with these by first week. Limping around for a week or two is common. Many can do mild to moderate activity in 10-14 days. Best by 4-6 weeks.