carpeperdiem,
Thank you for your interest.
Disabled and hidden products do not count. Products with multiple options/variants count as one product.
The countdown clock as well as displaying other subscription info is on our development plan.
You can see actual indexable product count via link like
http://cloudsearch.x-cart.com/demo/cloud_search_api.php?method=info (it's the link for our CloudSearch demo). It outputs json but it's pretty easy to see number of products in the response.
Re-indexation happens every 8 hours.
As for the search experience for a specific store I think it's better to discuss it via PM or in a HelpDesk ticket. At least I need to know which store we are talking about.
As for the exceptions, for now we rely on the stemming features provided by underlying Lucene library. Adding global/per-client exceptions support is also considered as a feature for the upcoming releases.