I agree with a lot of the sentiment in this thread.
First: lifting with a blister is no big deal as long as he's not sloughing off more skin around the blister. You should probably wash out that wound and fill it with neosporin or other antibacterial ointment then slap an adhesive bandage on it.
Second: Lifting schedules don't seem quite right for a 7 year old kid to me, but he's your kid, and as long as you supervise and he doesn't get hurt, there's nothing inherently wrong with it.
......however......
Children before puberty don't have the muscle differentiation as adults. That's why fit little kids all run about the same speed. Maybe 1 or 2 are faster, but overall, they're pretty similar.
Weight lifting when kids is a thing that was done in the old USSR. Children would lift weights, and do whatever other sports when really young, and got sent off to sports schools to become olympic athletes if they showed tremendous promise. However, the kids would only lift very light weight for form until puberty. Or something like that. i don't really know how their training programs work.
so, the summary of my ramble: make sure he stays safe, and don't let him get discouraged if he doesn't develop improved strength. His body isn't set up with the right hormones for hypertrophy yet.
Oh, and 100% don't let him take steroids. At that age his growth plates will just seal, and he'll be a buff little person. But you probably don't have to worry about that one.