Probably. Although I'm more familiar with Orthodox Christian monasticism, but yeah, depending on the monastery they'll take in visitors and belief isn't required, though a certain level of respect and open-mindedness is. Monasticism also isn't so much about 'studying' as contemplation (it's actually quite similar in some ways to Buddhist meditation). Not every monastery is open to visitors (depending on their facilities and number of monks), but it's worth sending a few calls/emails.

Probably, yeah. Look up monasteries in your area, there's a good chance there will be one with guest accommodations, and I gather you'd have access to their books, able to attend services if you want, etc. Details vary I'm sure. I've never done it myself but thought about it.