About email contact with prospective advisors who are yet to join the institute
I personally would be a little too concerned about a graduate student who keeps trying to "hard sell" themselves before I arrived. Partially this is because, if I were just starting a new position, I'd be worried about a million things, including winding down my previous employment situation, preparing for a move, figuring out all the different things that have to be done in the new position, and so on. Others may very well be different, though!

Note that I don't think it's wrong to be active when you sense a good opportunity, such as working with a scientist you hold in high regard as an advisor. However, being too aggressive may be just as damaging as being too passive. Steer clear of both extremes. For instance, have the advisors in question asked you to send them weekly updates? Have you asked them to  schedule a phone or Skype chat? Do you know if they are even "at home" or if they're on travel when they're not responding?

Advisors have their own personal styles, and your style should mesh with theirs. If it doesn't, it will likely be an unproductive and unhappy situation for both of you.