You got a lot of good answers already. So I won't go into all that. But I'll just pass you a couple of links that might illustrate what you are thinking about.
The "Green Book" series the Center for Military History put out a number of years ago is an excellent series and you can find them online nowadays. The 2nd link below lists most of them that can be found there.
1) Go halfway down and you'll see maps and click on #VIII (8). This shows you where the Airborne troops landed the morning of 6 Jun 44. Additionally, it shows you the dropzones (DZs) where they were suppose to land. So you can see the dispersal caused by incoming flak the planes took. There are some other good examples in that section of perhaps what you are looking for.
2) This is a listing of many of the military historical books (on-line) this website has (from the Center for Military History). It's a good list and they are very informative and exhaustive (almost to a fault). Good for any historian.
3) The website's main page
I have many of the books (received them while in the Army) and the maps are excellent as are the books. Seeing them online is real nice.
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2nd try...
There are military Field Manuals (FMs) that illustrate how a squad or any size element should theoretically be positioned in any number of situations. However, as one has already mentioned the real-world placement of troops depends on METT-T (Mission, Enemy Terrain Troops available, and Time).
You might find something at http://www.army.mil/usapa/doctrine/7_Series_Collection_1.html. It is a collection of FMs for the infantry. They are in .pdf format. Additionally, you might find some older FMs on ebay or at army surplus stores.
The examples I gave you above regarding the laydown of airborne troops during the Normandy Invasion may also answer your question as to how far apart larger size elements were from each other (larger than Fire Team but smaller than Company or Battalion).
I was an Intelligence Analyst in the Army and when I first came in we studied Soviet military theory in depth and learned how they moved in various situations (where squads were, etc) but this was in theory. The next step was to take that "doctrinal template" and lay it against the terrain and see where they might be realistically. You had to take the weather and no-go/go terrain into account and other various elements. It was pretty interesting stuff all-in-all.