I think the problem you're having is mainly syntax related. If you have a variable named $foo, ${foo} references the same variable. So, the ${table} and ${schema} references in your sql string work ok.
The issue is with ${col.column_name}. Your variable (I assume) is called $col, and has a member named column_name. As Robert and Steven both indicate in their answers, to refer to this, you should use $($col.column_name). In general, $(expression) will be replaced with the value of the expression.
The reason for allowing braces in variable names is so that variables can have unusual characters in their names. I would recommend not using the ${} syntax (unless you have a compelling reason), and replacing it with straight $var references for variables and $($var.member) for member references in strings.