IIS 7.5 Web.config Error from Wrong Application

I believe the assemblies entries are inherited down the chain of configuration. So, if you do not want your subdirectory application to try to load assemblies that do not exist, you need to add <remove> entries for those which do not exist. You would add those in the web.config file in the subdirectory.

With regard to your second question about how to ensure that configuration changes are persisted to a site's web.config rather than applicationHost.config, this can be controlled via Feature Delegation.

If you navigate to the machine node of IIS Manager you will see an icon named "Feature Delegation":

Launch this IIS "applet" and you will be presented with a list of features that can have their configuration delegated to web.config.

Settings that are marked Read/Write will usually have their settings written to the web.config file. Settings that are marked Read Only will usually have their settings written to applicationHost.config and cannot be overridden in the web.config file.

As it so happens the <windowsAuthentication> configuration can be delegated to the web.config file.

Minor Gotcha:

Not all of the applets surface the full range of settings you can configure. A good example of this as it so happens is the <windowsAuthentication> useAppPoolCredentials attribute. It's no-where to be seen in the Authentication applet, not even under Advanced Settings.

However you can get at this value (and pretty much everything else) via the Configuration Editor. If you navigate to your web site's node in the left hand pane in IIS manager you will see this icon under Management:

If you launch the Configuration Editor you'll be presented with a dropdown list containing a tree of various settings:

If we select the /system.webServer/security/authentication/windowsAuthentication node we are presented with the full spectrum of settings that can be changed. Here we can see the setting we're interested in (useAppPoolCredentials):

You can choose whether to configure the values for the website in web.config or in applicationHost.config from the From: drop down list next to the config section tree drop down:

If a section has not been delegated as Read/Write in the web.config then you'll see the following:

We get an alert saying that this particular feature is locked, all of the settings are greyed out and disabled and there's a padlock indicating that child settings of this feature are also locked out.

Finally, not all settings can be delegated, for example site bindings, application pool, virtual directories.