Slacks implies pants of certain materials which are not part of a suit (jeans are not slacks, and you would not refer to the pair of trousers that came with a suit as slacks.) It is also more common to use slacks to refer to pants worn by women, while men would wear trousers.
Health care safety net providers are those that have a legal mandate or mission to offer medical care to all patients, regardless of their ability to pay, and have a substantial number of patients who are uninsured or on Medicaid.
Since the med pay money is coming from your client's own insurance, the med pay insurer is going to be seeking recovery from the third party settlement. But note that if the claim is pursuant to an Underinsured Motorist (i.e. the third party had a limited policy, and you are now making a claim to your client's own insurer), the insurer may be entitled to a credit for any med pay amounts paid.