1. At what point in time would the copy be made? Would it grow older, or could I be 70 years old looking at my 20 year old copy?
I suppose the copy could be made whenever, but I'm currently envisioning a "current copy" (that is, if you make a copy now, the copy is "up-to-date," and there isn't a way to make a copy that represents you 20 years ago). But that's just how I'm envisioning it, there's no reason you can lead yourself on a thought experiment that's a bit different.
2. Given that our real-world experiences shape our personalities and behaviors, wouldn't we both travel different paths to become completely different people?
Yeah, pretty much. That kind of happens in Caprica. You could, of course, always "re-copy" yourself and update all your digital copies if you wanted to stay in sync. You could also have a "live-feedback" system where you and your digital copy are always connected, continuously sharing your... brains or whatever... so that the two of you are always up to date with each other (but of course you could still evolve differently).