Like others have said, it sounds as though you're doing great.
One thing I will add is this: go with cues your child gives you. If they get irritable re tummy time then don't push it. Our local baby gym does not accept children under 1 so we didn't do this but like Lulu has said, we didn't need much to entertain him anyway. My son didn't enjoy or engage in tummy time until he was nearly 5 months old (but loved lying on his back playing with the mobile) and is developing very well.