Most universities prefer to take and fund students starting in the fall. Occasionally some schools might take people in the Spring if for some reason a spot opens up, but the top schools tend not to do this, and the only way to find out about spring admission is to contact someone at that school.
PhDs are almost always funded, regardless of the school. Many good schools take funded masters students too. You can usually find information on the website of the department for that school. But as far as I know, there is no grand list of schools with funded masters programs.
