I'll do my best, but you'll have to let me know if I'm pointing you in a way you hadn't intended to go.
First off, you're a little bit off track. PRE-offer, you'd do best not to ask any job applicant that you didn't ask all the other applicants for that same position. POST offer, you have more freedom, and you can let your questions be guided by the answers of the questions that came before.
While you CAN ask just about anything you want post-offer, as an old hand at HR I would advise not asking any question that you don't really need the answer to. Anything you don't ask about, you can't be accused of using in a negative employment action somewhere down the line.
If it is your policy to have all employees (or all employees in certain position) to take a medical exam, then by all means have them take a medical exam. And if you get a result that raises questions about the employee's ability to do the job s/he was hired for, then by all means, go ahead and ask whatever questions it takes to determine whether or not they can do a job with or without a reasonable accomodation and what would be a reasonable accomodation if needed. You do NOT need to ask these same questions of other employees in that position, or other newly hired employees, who did not have questionable results.
The same applies with any drug testing.
But do you really need to know if they've had any previous workers comp claims? You MAY, depending on what you find in a medical exam, need to know about previous injuries for purposes of ADA compliance, but do you REALLY need to know if they were work related or not? After all, it's the end result that matters, not how they were injured in the first place.
Bottom line: Post offer, you can ask anything you NEED to know, but unless there is a valid business reason why you need to know, or a company policy (such as drug testing) that applies to ALL employees, the less you ask, the better off you are.
There are plenty of employees who, years down the line, remember that they were asked a particular question initially and accuse the employer of "waiting for a chance to fire me" based on the answer to that question, whatever it may be. Don't give them any more opportunites than you need to.