Are you removing the pages or just trying to de-index them? If you're trying to remove them, make sure the old pages return a 404 so they can't be restored to the index. If you're trying to remove them, make sure they are excluded by robots.txt or meta tag.

Here's the WMT Help page on the topic

http://support.google.com/webmasters/bin/answer.py?hl=en&answer=1663427

Good stuff. I was always under the impression they still crawled them (otherwise, how would you know if the block was removed).

Robots.txt prevents indexation, not crawling. The good news is that Googlebot stops crawling 404s.

Except for geolocation purposes, your IP has no real effect on your SEO. The only thing I would suggest is making your TTL on your DNS records very low about a day before you move so when you do move you minimize the chance that you're hitting the old IP.

Let's back up here.

You have a direct competitor with 60ish DA. Is that competitor a direct competitor (like Oreck and Bissel) or an indirect competitor (Bob's TVs vs Sears)?

I've been hearing this for years and it's always the same thing: Google likes .edu but not because it's .edu. EDU sites are typically major link bait in of themselves and they also don't link to other sites on a whim. As a result, they wind up with high site popularity and great link juice.