With the Level 1 doctor, he might still have an injury of 7 or 8 weeks.
My first major injury was to a 20 YO, who suffered a +4 week injury. I checked for a new doctor, and there a +9 available, and I actually caught his nurse raising his salary to almost $20,000. So I waited a week, during which my 20 YO was still at +4 injury. I then hired a "6" doctor. After that it took about 5 days for each week of injury. After I had hired the doctor, I had a 24 YO get a +4 week injury. With a "6" doctor it is still taking about 7 days per week of injury,
With your 22 YO and a "7" doctor, I'd expect perhaps 5 days per week of injury. Your player has been injured 12 days.
I agree with you about the stamina. It will take you a week or so just to get him back into game shape enough to start, and another before he really plays at his capabilities. I think that players should be able to improve low level stamina simply by playing in games. Playing 48 minutes/week might eventually lift a player up to average. You would still have to train a player if your really wanted to get him to higher levels.