I don't believe you can find out if someone is using Webmaster tools or not. However, you can easily check to see if they have a sitemap by  filetype:xlm sitemap site:domain.com (you may have to play around with this). Also, this doesn't mean it has been submitted as well.

It is a factor.  In general, It is easier to rank for a keyword on an older domain name than a newer domain name if all things being equal.  However,  great content and the ability to generate inbound links and etc will win in the long run.  Remember, Google's focus is show the most relevant results to the user. A factor of this may take in account that if a website is brand new (a month or so) it may not be as "credible" as a site that has been for a few years. Take a look what Matt Cutts says from awhile ago (should still be applicable).

IMHO, whatever the prospect is more likely to query use that in your url since it will be highlighted. I would probably not group them together as it makes the url a bit more difficult to read (so options 1 and 2 will work). Furthermore, whatever you chose I would put in the meta description "Human Capital Management (HCM)..." in case the prospect choose one or the other and include both variations on the landing page.

**Also, although I would also be curious to know if a subdomain inherits DA from the main domain, it probably doesn't need to be a part of the decision making process for choosing between subdomain and subfolder.  **

I know that the sub & parent share the same DA. I was under the impression that one doesn't necessarily inherit the other DA, just an accumulation of the "strength" calculated by Moz of the domain shared between the parent & subs.