Joining the group at a later date is difficult and rarely done due to academic considerations. Staying longer depends on the airline carrier and their rules which are not always consistent. Determination will be made depending on the airline carrier in use. There are a number of free days scheduled, plus students often do personal touring before or after classes, homework permitting. All the cities have relatively inexpensive mass transit systems available.
Grocery stores are available in all locations.
Affordable local restaurants are generally available. A limited number of meals other than breakfast will be part of the scheduled tours. Buy a good converter set and try to keep to a minimum the number and types of electrical appliances you bring. Several hair dryers and shavers blew out on last year's trip. If you get lost, you can always use the local taxis to get you back to the hotel.