Pinegrow is a great tool for web design. You can also easily convert plain HTML projects to WordPress themes. More recently one of the designers at Pinegrow put together a tutorial together for converting a WordPress theme back into a static site. This allows you to use a local server, like Local, MAMP/XAMP, and WordPress CMS to create content, but then use plain hosting to serve your pages. Here is a link. Working with an existing theme in Pinegrow is possible, but Pinegrow isn’t really designed with this in mind.
Based on your second question, I just want to clarify that Pinegrow is a web editor. It helps you build sites quickly with a large number of visual tools to reduce the amount of coding that must be done. It does not host the site for you. That must be purchased separately. With respect to 3rd party themes - as long as the code of the theme is not malformed, you should be able to work with it in Pinegrow.