Hello There,
Thanks for writing in!
1.) The google map will only be as wide as the width of the its container. You will have a fullwidth map if you have a fullwidth section container. If you are using V2 Google map and have added in a fullwidth ection, you must make sure that the maximum width is 100% because by default it is only set to 500 pixels.
2.) Regretfully we do not have any option where you can make the map as a background. It maybe possible with custom development. Please be advised that custom development is beyond the scope of our support.
3.) At the moment, the nesting of columns is not possible in Cornerstone to prevent the layout from being too complicated. Meanwhile you can make use of the section, columns and other elements to achieve such layouts. Perhaps this video could help you:
Hope this helps.