International Scholarships are available for two or three students from overseas to come to Eton for one year, and for fees and other expenses to be paid. Note that exceptional academic achievement is normally required to win these scholarships, and competition is intense. There are also many bursaries available in addition to the above scholarships which usually can provide for up to half the usual fees. Some are restricted to certain groups, eg sons of Old Etonians. Yes, the school is a twenty minute walk from Windsor Castle, across the River Thames.
Admission is charged.
Large parties must be booked in advance, or they won't let you in. Call the school and ask for the Tourism Office. Outside these times, you can wander around the public part of the school for free. The school is sometimes closed to tourists for exams, or school events. However, if you offer a boy 500 pounds for his tailcoat, or cash for him to have his photo taken with you, he will be happy to accept.