To answer the title question, yes you can store settings in a separate config file, to do so you need to define the configSource
property of appSettings
element
E.g.
<appSettings configSource="settings.config" />
and in the settings.config file
<?xml version="1.0" encoding="UTF-8"?>
<appSettings>
<add key="settingKey" value="environmentValue" />
</appSettings>
However, for the sake of environment specific settings, you may want to look at config transforms. Setting up a transform config for each environment then deploying to that environment with the specified build configuration.
E.g. Web.Dev.config (provided you have setup a 'Dev' build configuration)
<configuration xmlns:xdt="http://schemas.microsoft.com/XML-Document-Transform">
<appSettings>
<add key="settingKey"
value="devEnvironmentValue"
xdt:Transform="SetAttributes" xdt:Locator="Match(key)"/>
</appSettings>
</configuration>
More details of build configuration and config transforms here: http://msdn.microsoft.com/en-us/library/dd465318(v=vs.100).aspx
Or you could take advantage of TFS features and parameterize the environment variables, I don't have a lot of experience with this, but the following should help: http://ig.obsglobal.com/2013/02/tfs-and-continuous-deployment-part-4-parameterized-deployments/