Submit Expired Pages in XML Sitemaps
You can submit an XML Sitemap with expired pages to help get them removed from the index more quickly. It’s best to put them into a separate sitemap so you can see them separately to other indexable URLs.
Mobile Sitemaps Are Not for Smartphone Pages
Mobile sitemaps are for feature phone pages only, not smartphone compatible pages. If you have smartphone URLs which are different to the desktop URLs, use a normal XML sitemap with rel=alternate.
Change Frequency and Priority in Sitemaps Are Ignored
Change Frequency and Priority in XML Sitemaps are not used by web search, but the lastmod date is used.
Submit Sitemaps with Changed URLs
If you change many URLs, you should submit a sitemap with the old URLs to Google which will help them pick up the redirects to the new URLs. Webmaster tools will report errors with the sitemap, because it only contains redirecting URLs, but this is fine.