Check the following document about resource mapping to define redirects, vanity URLs and virtual hosts for AEM.Resource Mapping

You can use the  /statfileslevel  property in dispatcher configuration to invalidate cached files according to their path.Configuring Dispatcher

See the following document: Customizing Pages shown by the Error Handler

Also you can perform a force a recompilation of all Sling scripts jsps, java, and sightly:How to force a recompilation of all Sling scripts jsps, java, and sightly in AEM 6.4

If you are connected to the instance as an admin then you should have access to the /conf directory. You may want to double check that you have Create, Modify, and Delete permissions on the /conf folder. This can be checked via user/group admin console: http://host:port/useradmin

I am not sure about moving from 5.6.1 to 6.2 but there has been repository restructure moving to 6.4 including the location of etc/tags [1] so the same may have happened in the older versions but I never worked with those versions so I am just giving you an idea that its entirely possible that the s...

In your initial question you mentioned "would like to rollout the fragments to other locals" that means translation. So content fragments are assets in nature so they can not be rolled out individually if that's what you mean.

Do you have any ACS common package installed that may have caused a conflict ? If so check the "error.log" to find out if there has been a conflict. 

1. Make sure the translation integration configuration has content fragment translation enabled.2. Content Fragment content is present as property main in the crx repo. You would have to add this property in the /content/dam context in translation rules for the content to be translated.

Please provide the version including the service pack. The reason is to verify if a known issue has been fixed in a certain fix pack so we know if you have the fix in your instance. Also I am assuming the template a an editable template (?)