Yes, i think, it is important to set it XML sitemap because on the basis of that crawler crawls your pages & gives importance.
mmm not important if you just need to submit a sitemap to index your URLs on search engines.But if you are planning to grow site traffic and ranks...etc.You should create a crawler friendly sitemap by including all of it's components. Regards.
Although Google recommends the use of these settings, we have found that only the "lastModDate" is used.
It's not important at all. It comes important only if very slight changes can help you to gain much more traffic. So if you have 2 pages, and google crawls the less important more often (you can figure this out by checking google's cache date) you can set your more valuable page to a higher priority. So it worth to be set up when you create your sitemap, but does not really worth any further efforts.