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Also, here is the best place to answer your questions.

From Google:  "The Test robots.txt tool will show you if your robots.txt file is accidentally blocking Googlebot from a file or directory on your site, or if it's permitting Googlebot to crawl files that should not appear on the web. "  You can find it here

If you are wanting to continue to link to the old domain within the old domain but remove any hits from the new domain I would simply put a canonical tag in the old domain designating the new domain as the content source.  This way you can continue to use it and link to it within the old domain to allow a unified UX and give full SEO credit to the right spot.

I meant include this robot in the subdomain not include the subdomain in the robot.  Was answering an employee at the same time and crossed some wires.  

What you ideally want to do is set up the mobile site as a standard site.  Then utilize javascript to call each page in an order defined by the users actions with dynamic loading.

This has two benefits:

1. SEO and SERP.  The pages will be indexed as they should.  If you have one huge page you are still limited to the 2 or 3 keywords as always.  When you see a good infinite scroll website it is not one page, it only looks this way due to JavaScript calling additional pages at triggers that have been set.

2. No JavaScript graceful fallback (or fallforward as it is actually the native state).  If you have one page, lazy loading with JavaScript and they do not support it then you have 2,000 pages worth of images loading at one time which is otherwise known as a bounce.

You will want to build out the site with no consideration to the infinite scrolling (except in design ie. tile-able backgrounds for a smooth non stop flow) then apply the script after you have a logical site structure using silo'ed categories.  Google bot, Google bot mobile and users who do not have JavaScript will all have a useable site and the SERPS will rank pages as they should.

Tip:  Keep any page wide bar or graphic styles in the header or the footer of the page.  You will normally only call the content or article portion of the page to the infinite scroll so you have a non-stop flow on the site.

Hope this helps

I know your not using WordPress but I am assuming you are using some sort of templated PHP script for a 2K product store.  This WP plugin is pretty easy to understand and what I first used to grab the concept.  Also, if wanting to go a more Pinterest route look into Masonry JavaScript.  http://www.infinite-scroll.com/

By the product segments not being directly related, I would ask how indirect is the relation?  Are we talking Fresh Produce and Cars or Tablets and PC's?

I would highly suggest building a single site unless you have some regulatory factors that keep you from it.  Think of other eCommerce sites and the product diversity they have.  eBay, Wal-Mart etc.  There is a lot of variations.

You may want to put product information and blogs into separate folders for each product, so you build a clear set of data defining the products you sell.