I would like to know if sending a sitemap to Google means every page, including the category pages and the strongest ones will have the same power than other deep pages.
I heard that when you send a sitemap to Google with all the URLs what you are telling Google is that every page on that sitemap is on the same level of importance (category pages and deep pages). Is that true?
I would like to clarify that before sending a sitemap to Google. I don't want to tell Google that pages which are one click from the homepage are as important than the ones which are 3-4 or even more clicks from the homepage.
Google uses sitemaps as a way for webmasters to suggest urls for inclusion in the Google index. They do not follow sitemaps exactly as they are submitted. If they did that too many webmasters would abuse it and too many other webmasters would innocently hurt their rankings.
The best way for you to tell Google what pages are most important is by having the most amount of links pointing to those pages.