If you received your COBRA information in mid-June, promptly requested the continuation of your benefits through COBRA consistent with the information provided, and have heard nothing back for more than a month -- no information about premiums, no indication that your application was received, nothing that would indicate that your insurance has been reinstated -- then you need to be a lot more diligent about following up with HR.
If you want to know whether your doctor will release you to return to work on a trial basis, you will need to ask your doctor. That's not a legal question.

