1. A 9 week puppy may be tired after playing and not want to play. Before you take him to play, you might try a little play at home, possibly shaking a cat toy, or a length of rope, dragging it back and forth on the floor in front of him to get him interested in the motion. ... In about 3 more weeks, he will be more interactive.
2. With lure training, at 9 weeks, you are probably lucky to get 5 minutes of attention. Again, in about 3 more weeks, his attention should improve. It is OK to teach him for 2 - 3 min., let him play or explore, then teach for 2-3 min. more.
3. Ask your friend about putting on his collar, then letting the dogs play. The play distraction may make him ignore the collar enough to get used to it.
4. If you carry him, he probably won't get tired. If you have a backyard, and you run from him, does he ignore you?
5. Separation anxiety is a situation where the dog gets very scared and anxious, tearing things up out of frustration. Nothing that you describe sounds that extreme, or even "velcro dog" where he wants to be around you all the time. He's probably just a very young puppy that can't run very well or see very well, yet.
6. It is OK to carry when you run errands, but in the yard and house, try not to carry him like a stuffed toy ... make him walk and follow you himself ... Or put him away in the crate, if you can't watch him, while you are training him not to potty in the house. It's OK to sit with him while you watch TV or the computer...