I'm running online store with 30,000+ products (having unique urls) which are updated every day. I want google to index my products faster. Now crawler index ~500 pages/day (reports from google webmaster tools). Would generating sitemap xml improve indexing? Should I include in sitemap static pages like contact, shipping info etc (I have about 10 such pages)? Does google bot works independently and index pages that are not listed in sitemap?
In theory, but there are no promises, either. ("Google doesn't guarantee that we'll crawl or index all of your URLs." etc.) Sitemaps can be helpful for bots to find all your pages, but they're informational; they aren't required to do anything with them. The search engines may decide to disregard some documents for whatever reasons of their own.
There's no real reason to leave any URLs out.
Yes, all the spiders do. Sitemaps are only there to help them do their jobs, especially for documents that may not be linked yet, or not very well.
It sounds like your type of site was exactly what the Sitemap protocol was created for. I'd say that a sitemap file could do nothing but improve your site's indexing.
Adding your static content is also not a bad idea, and you can use the
It's also worth looking into tools like Google Webmaster Tools - Google in particular have a section where you can tweak your crawl settings to see if that helps.