Visually speaking, is it possible to make my ads look exactly like that screenshot? In terms of the full width of the 3 ads combined, the width of each individual ad, as well as the spacing between each individual ad?
That depends on the space you have to work with. Adsense ads are standard ad format size, used across the web.
You can see the various ad formats here and their corresponding sizes:
In general, adsense ads don't "look like" the sample ads you posted in terms of style.
The wizard allows you to customize the colours, so the "border" colour can be the same colour as your website background, effectually giving an ad with no border, as can the background colour and text colours.
And some ad sizes will have more than one advertisement in them so you'd probably want to stick to the smaller sizes if you only want one ad in each.