Week1/Month1 means that their tax credits and rate bands are not operated on a cumulative basis for the year - you just apply the weekly/monthly amounts to their weekly/monthly pay as a separate calculation each week/month.
If they have a valid medical card levies do not apply. It is not up to the employer to check on their situation. However, take a copy of medical card for your records, and ask the employee to advise if you this is withdrawn (do that in writing). You are then taking care of your responsibilities.