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No, now that they have offered you the job and if they were to withdraw their offer due to your medical condition you would have strong grounds to sue.
No, they do not usually do a drug test prior to offering. They want to be sure you do not use illegal drugs. If your medications come up on the test, you should be able to provide proof of your prescription or doctor's order for such medication.
My answer still applies. As long as on the application you did not mark that you had no disability that would require accommodations.
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