Unless the layout was changed or things went wrong, no. I've migrated maybe 50 websites over the past year with no ill effects. Any that did, occurred because something went wrong (htaccess issues, extended downtime) or because there was a design change. In the case of the latter, rankings return any time between a few days to a few weeks. (Assuming the markup/content is still good)

http://pingomatic.com/ is a very popular one. Keep in mind that many platforms such as WordPress do this automatically for you.

If you need a larger list, you should write your own script to do so. Pinging a list of URLs would be very easy to do. Ping O Matic should do the job, however.

As far as using a browser addon, why would you need that?

You're essentially asking if sitewide links are OK. Yes, they are.

Marcus makes a good point: if any of the pages are poor in quality, you'll notice a decline in value. Your priority should be ensuring all of the pages are high in quality, or at the least noindexed. The problem with WPMU was that they can't control the quality, so they just took the links out. Sounds like you are in a position to keep the links, but do a bit of cleanup.

The virtual host is what tells your web server (Apache) basic details about your website. Where to find it (path), where to store error logs, the domain name, and so forth.

Unfortunately you will need a developer to do something for you if you aren't too sure about how to go about the process, and especially if you aren't familiar with Linux platforms.

I'm not suggesting to get a hosting account for every domain -- addon domains are perfectly fine. Just make sure you are redirecting correctly (whether through .htaccess or through cPanel config). I had well over 100 addon domains many years ago when I still used cPanel

You should have both. Keep the paged navigation at top, but keep the infinite scroll. Now you have the best of both worlds.

Although, I don't think the infinite scroll would end up 'delinking' thousands of pages. How often do you see store.com/category/page/6 in results, anyway? If it's a popular term, it's going to be for the main category landing page.

Serving up different content to Google is always a bad idea unless you have a good reason. This problem doesn't qualify.

I'm assuming you are using cPanel? You are able to enable redirection within your panel. (I haven't seen this issue outside of cPanel)

Ideally, you are right, you shouldn't have mirror content up. If you can edit the virtual hosts on the server directly that would be another option.

Perhaps the better solution is to check referrer data in the header of your new domain, and show a brief note at the top of the page if it's from your prior domain. This has the benefit of not annoying your visitors with a wait time (a big deal) and you don't have to count on a workaround being fine with Google.

Simple to do in any web language, let me know if you need help.

I wouldn't slow the crawl rate. A high crawl rate is good so that Google can keep their index of your website current.

The better solution is to reconsider your hardware and networking setup. Do you know how you are being hosted? From my own experience with a website of that size, a load balancer on two decent dedicated servers should handle the load without problems. Google crawling your pages shouldn't create noticeable overhead on the right setup.

What Schema data are you referring to? Different microtags will apply to different pages. Generally, anywhere you can use a microtag, you should.