I don't think it matters how close to the deadline you apply as long as everything is received by the programs before the deadline. I haven't heard of any programs that do rolling admissions, but it doesn't hurt to check just to be sure. Regarding CVs/resume and personal statements, check what each program requests. The websites specify how long the personal statement should be.
Regarding responses, it depends on the school. Some schools will let you know right away if you haven't been selected for an interview, and others will wait until after they have accepted students. If you're applying for Fall 2014, you should hear back by March/April. Most schools usually have interviews in March.
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