If I add settings to my app's web.config file, is there an API to read the settings from my app or do I have to read the file using an XML library?
There is no special API that allows you read web.config into your node.js application running in iisnode. Having said that:
This example shows how promoted key/value pairs from the appSettings section in web.config are available as environment variables. In your web.config file:
<configuration>
<appSettings>
<add key="abc" value="test" />
</appSettings>
</configuration>
In your node application: console.log(process.env.abc); //--> test