This is not an unusual situation for residents of the US, often parents buy a house as an investment and have their child/student manage the rental of the property. I can't see why it would be any different for an F-1 Visa holder. So it is not legally complicated.
Real estate is probably the best use of funds right now, saving you the cost of a dorm or apartment, and generating income from other students.
Just a couple of suggestions, when you rent to the other students (tenants) set up an account with your bank or Paypal so you can accept a credit card, VISA is the cheapest and most common. Take their parents card as a deposit, then if their rent is late or there are physical damages, you will have recourse, and can charge the credit card.
Buy a property with multiple bedrooms, (3 or 4) but don't rent to more than one person per bedroom. I have had issues with students saying that they were sharing a room and paying their half, but their roommate moved out, so they thought they only owed 1/2 the room rate. This is always an issue. Rent each bedroom to one person.
Don't let them rent just for the school year, make your tenants sign a 12 month lease and pay you even through the summer, but let them sublet the unit to a summer school student if they are not going to be in residence. The primary tenant will be responsible to you for the rent, the sub-let tenant will pay them.