Horizontal style drop down boxes

It could be possible. There are forced line breaks between the label and the available selection which may be rendered by, per source, Mac's ThisNThat Search Widget. So if you can access that widget source files, and delete the <br /> between the labels and selections, you’re good to go.

Otherwise, since you’re using a premium theme, I would suggest contacting theme author for assistance. Most probably the same issue might have been resolved in authors forums if any.

I’ve revised the sections – adding breaks and div class surrounding the three sections
// First the Top DropDown Parents
// Now the Middle Parents
// And the TopParents Children.
and pasted the revised sections here.

Add these to your theme’s style.css

li#mtswwidget-5 select, .mtswlabel {
font-size: 12px;
}

.columnar {
width: 32%;
float: left;
}

adjust font-size to taste, but not too large or the other column will drop down to a new row

this works, because everything to be echoed is with in the double quotes, and is using single quotes for the class:
echo "<br /><span class='mtswlabel'>$top_label</span><br />";

your other line is mixing the quotes, and the first double quote of the class="columnar" breaks the echo string:

try:
echo "<div class='columnar'><span class='mtswlabel'>$top_label</span>";