Does Elven Map Redux effect the Local map? Does it color the Local map?

AFAIK it doesnt, but there is an .ini tweak you can apply to remove the local map shader.
In your .ini find the line blocalmapshader=1 and change it 0.

No, it definitely doesn't.
Johnn123 gave the correct Oblivion.ini tweak.
The tweak can also be added in Wrye Bash under the "INI Edits" tab.

You may wish to check out http://www.tesnexus.com/downloads/file.php?id=35969. It uses the Elven Map (among other options) and includes map components from certain mods.
If you have any of those mods, your map will then be more true to your game.