Good questions dude,
So for the first thing, it is MUCH more worthwhile that you simply apply ED. I'm not sure what you are doing in your EC, but still, the difference of a few months is not likely to outweigh the advantage of applying ED, which if Columbia is your target, I highly suggest.
Second, doing anything you can to show interest is fantastic (talking to students, alumni, professors, more research etc.), visits can be excellent too, buuuut I don't want to give you the impression that "if you visit you will have better chances" because it's just not true. Yes, it helps a wee bit on the feeling side, it helps you also deepen your knowledge about Columbia which in a very indirect way can be beneficial too, so it may be worth it for other reasons.
Hope this answers your questions...
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