Does your company have a written policy about employees who admit to drug use?

Ours states: "the driver admits to use but requests assistance, the alcohol and drug program administrator will supply the employee with information regarding an appropriate substance abuse professional (SAP). The employee will be put on leave without pay for a minimum of 6 weeks. If the employee successfully completes appropriate treatment including successful in passing a drug test the employee may be rehired at the company's discretion."

So the answers to your questions are:

You have every right to make sure that the individual is not currently using drugs. Some drugs stay in the system longer than others so a long enough time needs to pass for the drugs to be out of their system.

I would ask for paperwork from the Substance Abuse program stating that they have successfully completed the program which may or may not include a negative drug test.

If the program didn't test them then yes send them for a test and monitor them closely. Decide how often you want to test them (once a week or every two weeks) and do it for a reasonable amount of time (one month to six months). This gives them sufficient time to prove themselves to you and the company. Later on if there is a reasonable suspicion test them ASAP.