First & for most your request is "/bin/replicate.json" sounds strange it is using fallback Command Servlet. That means aem content management related bundle are missing or not satisfied. I would look more into bundles state & logs before the issue occured. Or blindly try with rebuilding launchpad. I...

https://forums.adobe.com/message/3995737

Evaluation is bottom up. Refer details at https://docs.adobe.com/docs/en/cq/5-6-1/administering/security.html#Access%20Control%20Lists%20and%20how%20they%20are%20evaluated

You might have to wait little more time to get support for 3.0.4 [1].    If you have tight project lines please engage with support through daycare to get the attention.[1]  http://docs.adobe.com/docs/en/aem/6-1/deploy/technical-requirements.html

Yes client context is not server side implementation & executes at client side. There is no out of the box java api available. You can use application server for session management Or need custom development by making use ResourceProvider.

You need to use mongo & with tarmk not available.  http://docs.adobe.com/docs/en/aem/6-0/deploy/recommended-deploys.htmlhttp://www.citytechinc.com/us/en/blog/2015/05/aem-6-x-mongo-backed-clustered-author-setup.html

http://felix.apache.org/documentation/subprojects/apache-felix-config-admin.htmlhttps://osgi.org/javadoc/r4v42/org/osgi/service/cm/ConfigurationAdmin.html

https://helpx.adobe.com/experience-manager/kb/ComponentDiv.html

Login at [1]. Then go to developer mode[2] and execute the script. [1]   http://host:port/libs/granite/core/content/login.html[2]   http://host:port/editor.html/<pagepath>.html    Ex:-  http://localhost:4503/editor.html/content/geometrixx-outdoors/en.html

https://docs.adobe.com/docs/en/cq/5-6-1/developing/mobile.html