No. The Sistine Chapel is INSIDE the Vatican Museums.The only way to see it is to go through the Vatican Museums.
It depends on what we mean for “the Vatican”. There are several options. If we see only St. Peter’s basilica, we can insert this tour in a city tour of Rome, and so we’ll need about 1 and 1/2 hour. In case we wish to have a complete tour, so to enjoy both parts of the highlights in the Vatican museums and St. Peter’s basilica, we’ll need around 5 hours.
No. The only ticket that we need is to go through the Vatican museums. Yet, in case we’ll enjoy only a tour of St. Peter’s basilica, we won’t need any ticket.
To enter St. Peter’s basilica, the rules are:
In the Vatican museums, pictures are allowed anywhere without flash, except inside the Sistine Chapel, where pictures are not allowed at all. Inside St. Peter’s basilica, pictures are allowed even with flash.