6-12 weeks. The time it takes to recover varies considerably depending on the person and the actual procedures done during the surgery. Arthroscopic surgery can be a simple bone spur removal or an extensive repair of a massive rotator cuff tear. In generally people are pretty sore for 2-3 weeks requiring narcotic pain meds. Most are in a sling for 6 weeks and require physical therapy 2x/week for 4-8 weeks.
Really depends. Many different procedures can be done to the shoulder during an arthroscopic surgery. If bone spurs removed, shoulder debrided, then pain may be minimal and pass within a few days. If cuff repaired or labrum repaired, pain can persist for a couple of months. Make sure you understand exactly what is being done during your scope. Don't compare your results with someone else's.