As a workaround - copy all files from under Carousel Core Component and place under you Carousel under your project under Apps. I just did that and it works fine.

YOU need AEM Forms Doc Services to do this. Adobe Experience Manager Help | Using Document Services in AEM Forms

Go through this article -- follow it step by step - it works. Then once you get it working - you can compare it with yours to see the difference.

Look at our SOLR Article. This one closely matches your requirement. We have a class named MySimpleService that reads OSGi config values. In the Servlet in this article - we use a @Refence to get config values:@Reference    SolrServerConfiguration solrConfigurationService;This shows the proper way o...

Like I said - create the logic to read OSGI config values in a separate class. Then create an instance of that class in the servlet and call a getter method. That will return config values in the servlet.

IF you want a reference to another site in your web page - assuming in the page's text - you can simply link to an outside URL using the RTE.

Are you seeing any strange behaviour in your page when you open it?

Lokesh is correct - AEM does not expose an API to perform a use case that you are describing. You would need to look at writing JS script. 

Following article shows how to read OSGi config values - notice this class is not a Sling Servlet: Reading OSGi Configuration Values for Adobe Experience Manager 6.3

That may be where your issue is. I would not try to mix that up. I would create a separate class that reads those OSGi conig values. Then from your Sling Servlet - you can create an instance of that class and invoke a method to get the config values.