Tracy Jennings, Works at Noodle and here to help!
Yes, Paul Cuffee School is just for students who live within the city limits of Providence, and yes, the kindergarten works on the same schedule as the rest of the grades.
When it comes to enrollment, Paul Cuffee, as a charter school, has a different process than your 'home' public school, which is dependent on which school zone you live in within the city. Instead, any Providence student wishing to attend Paul Cuffee must submit an application. The application period runs from November 12 to February 16 — see here for the admissions calendar in more detail. In March, a lottery happens for a certain number of open seats, and any students who are not selected are put onto the waiting list, in the order of which they were drawn on the lottery.
The Paul Cuffee website states clearly, "Parents of students who are not selected from the waiting list by November may re-apply for the next school year by submitting a new application at that time. In accordance with the Rhode Island Department of Education enrollment guidelines for charter schools, waiting lists will not be carried over from year to year. A new lottery is conducted each year." This means that if your child is unsuccessful at getting a place at the school in March 2015, you'll have to re-apply the following November for a spot in first grade.