Highlight entire row

Is it possible to highlight the entire row’s background color, from the far left of the div to the far right, instead of just the text portion of a node?

I’m not pretty sure what do you mean by "highlight"
If you mean just changing row color it can bo done by many ways
    from XML as <row bgColor=“red” …
    from JS API grid.setRowColor(ID,“red”);

If you mean natural selection - it is blocked by default, and can be enabled by small modification in grid code
    1. In dhtmlxgrid.css locate and erase all occurences of next line
    2. In grid initialization code add next command
       grid.entBox.onselectstart = function(){ return true; };