That was definitely the most commonly used liturgy book since the Coptic Church was established in the United States, but a lot of churches are now switching to the Southern United States Diocese's book available here: http://suscopts.org/diocese/bookstore/
which includes a much more modern, correct, and elegant English translation, a larger collection of the seasonal hymns and doxologies, and a much better binding (Fr. Matthias Wahba's book unfortunately gets unbinded rather easily). I know the Southern Diocese uses this new book as their standard, and I believe most of the churches here in NJ and the tri-state area are shifting, if they haven't already done so, to this translation. I do not know what the rest of the country's churches are using but I'm sure another Copt can chime in.
The churches that utilize St. George and St. Shenouda Church's Powerpoint for the services usually use the Southern Diocese's book as the powerpoints are based on that book, and they can be found and downloaded here free: http://stshenoudajc.org/index.php/Church-Services/About-Coptic-Presentations.html
The responses changed just a bit in the new translation but not so much that the old book is worthless, so you don't have to worry about your purchase, however, you may notice if you visit a lot of Coptic churches that each may have a somewhat different way of chanting the responses. Just go along with them and don't worry too much about it.
To answer your other questions, St. Basil's Liturgy is typically prayed on an annual-rite Sunday, though some priests will regularly insert some portions of St. Gregory's Liturgy during the service. St. Gregory's is typically prayed on festive occasions, while St. Cyril's is (rarely) prayed during the lenten season, as it is the longest liturgy, and unfortunately, a lot of the hymns and tunes have been lost throughout the last few centuries.