1. This is always the argument and it really becomes an issue of fact for a jury to decide if there isn't an agreement on when the injury occurred.
2. There is no law requiring notice, but failing to give notice of the workplace injury when it occurred makes the employee's position more difficult to prove. Ultimately, it is the employee's obligation to prove that the injury is work related. That being said, some back injuries are slow onset. This isn't like a bro***** *****d, which would have been an immediate trauma. The employer can make a policy requiring immediate notification of workplace injuries, but nothing in WC law requires that the employee do so in order to be WC eligible.
3. This is a very common complaint, with repetitive stress injuries. It's harder to prove for the employee, but doctors connect repetitive stress injuries to workplace conditions all the time.
Employer can state that they don't feel it is work related and force the employee to make the WC filing, get a doctor to connect the injury to the workplace condition and obtain a WC settlement for the medical issues (if he can prove the connection).
Yes, it is fine to require a release to work before allowing them to return to work. Nothing in law requires an employer to create a light duty position. The only concern you'd have here is if you have, in the past, created numerous light duty situations for others and are suddenly not doing it here. Then the concern becomes "how does this person differ from the others? Race, religion, gender, age, disability? Then they could argue discrimination treatment). This is the only concern though.