My Home page is an article. Is there a way in the Maximum template to provision a background image to it? I guess this would be the 'main-top' position.
Same question regarding the 'sidebar-a' - can it be given a background image, too?

Hello, of course it is possible.
But it must be done with css/custom.css style.
1.) Search the DIV > with Browser developer tool > www.joomlaplates.com/template-customizing
2.) Now add the css style to your css/custom.css like that

#sidebar-a {background-image: url("images/sample.gif");

www.w3schools.com/csSref/pr_background-image.asp

Thanks for the information. I downloaded the FireFox Developer browser, found the elements neded, and learned to be careful in creating the custom.css file. Seems best to delete the custom file and build a new one to assure all browsers render properly.

Problem solved.

Wondering how to avoid the caching of the custom.css file. I make a change in it, or create a new one, and one browser sees the change, another browser sees the old custom?

Hello, sorry depends on your Browser setup! And has nothing todo with the theme.
And please disable ALL caching ( Joomla & Browser cache) tools while you are developing a website