the menu data sources are synced automatically, the checkbox is not present to delete them see this forum thread also: http://storejextensions.org/forum/view/10-jsitemap/308-checkbox-problem.html
The 'content' data source has the checkbox if you enable the multiple content data source option in the jsitemap configuration. Menu data sources can be simply published/unpublished and are synced automatically when you create/edit/delete them in Joomla.
If you don't reflect a name change for a menu, ensure tho have reloaded the control panel of jsitemap after that the menu name has changed. There is where sync is done.
However you can override the name of the menu used in the sitemap in frontend, there is the field 'title' for each data source where you can specify a different name used for the sitemap containing folder.