Is it possible to add Facet and Sort components to 'Search View Layout WebCrawler'?
Only search results are available upon creating a page based upon 'Search View Layout WebCrawler'. Is it possible to customize this to add Facet and sort components? Reference - https://developers.coveo.com/display/public/SitecoreV3/Creating+a+Search+Interface+Optimized+for+WebCrawlers
It is, indeed, but this will require some work on your side.
The page has to be entirely built server-side. We have this tutorial, which explains how to build your queries using LINQ. You are interested in this page: It explains how to add facets. The sorts component are not really required since the page is for web crawlers (an image or some HTML could be OK).
I need to mention that this tutorial was written with the latest version of C4SC 4.0 (July 2016) and that some modifications were made to make it easier. In other words, this tutorial does not apply to earlier versions.
I also have to tell you that even though Coveo supports LINQ development, it is not a practice we encourage.