To answer the original questions.
Yes. You should meet with the coach and go on the school tours. Let son arrange the visit itself but once you're there feel free to ask questions about the school and the program. But try to let the kid do the talking. See if the school is fully funded and see what the scholarship covers. Is it tuition, tuition/board, tuition/board/books/etc? I also wouldn't ask for an official visit as they are reserved for committed seniors right before signing day
As for the time. I would say a week is fair. If it takes more than a week to decide, how interested were you in the school in the first place? Research the school and the program beforehand. Ask questions once you get there. And make sure it is a school your son would want to go to before the visit. No need to visit a school you have no interest in just for an offer. "Thank you for the offer, if it is okay with you I would like to take a week or so to go over the decision with my family." 30 days or more just shows the coach you're not crazy about the school and looking for a better offer.
Hs and travel coaches are great but they're just a foot in the door. Once they've created interest and helped arrange contact they've done their job. Good luck