I cannot find XLV web part. Is it included in SharePoint 2010 by default or should be activated/added manually? What web part category should it be placed in?
When you add a list through "Lists And Libraries" you actually add a XSLTListViewWebPart.
It is by default scoped to current SPWeb, if you want to create a web part of it you should be able to manually create a .webpart-file that points to a specific list (even on a different SPWeb).
You can also make your own web part and aggregate it, like this: