Do people with prostatectomy have a lot of pain?

Not usually. Pain is not typically a prominent feature of prostatectomy (assuming you mean radical prostatectomy for prostate cancer). Pain may be slightly less with minimally invasive (robotic) approach vs. Traditional open surgery, but perhaps discomfort is a better term in either case. Significant pain may be a potential cause for concern.
No. Most men who undergo a robotic prostatectomy take minimal medications for pain. Open surgery can be more painful, but after a couple days, you usually only need oral pain pills.
No. Except for normal post-surgical pain, no.
May. After the acute phase following surgery, patients should not have lot of pain unless there are complications like infection, bleeding or leakage of urine.