No, the number of applications doesn't seem to have decreased. We decided to do this back in Jan when we moved the application deadline earlier, because there's now a 3 month gap between the application deadline and when the cycle starts, and we know from experience that when people start startups, they don't always know they're going to 3 months beforehand.
We've thought about it. We may one day. But there is some stuff that usually happens between cycles, like organizing Startup School. Plus we need some time off. During the YC cycle we are very busy, like the startups themselves are, because time is so compressed.
Maybe a little, but I doubt it. Sounds like they've known this is a problem for awhile: someone decides to start a startup right after the deadline, hears about YC, wants to do it, but has to wait a long time (beginning of April- beginning of January is 9 months) to hit a cycle.
But by moving the deadline earlier, they made the problem that much worse, which got them thinking about the problem, which lead them to decide on this approach.
PG has said in the past that YC don't have an upper limit on the number of groups to fund. This isn't a zero-sum game: if having no deadline means they get more applicantions of which a steady percentage is fundable, then it's worth doing as long as they don't overstretch their resources.