How do I export/import all the relations created by Relation module? There are standard procedures to export/import relation types, but not for the relations themselves. At least, I couldn't find any. Am I missing something obvious?
Export/Import of entities is something that is not standardized and there are many methods of approaching the problem. This is also something Drupal 8 is attempting to solve.

Currently you want to look at Deploy and UUID Features are your best bet. Neither have stable D7 releases, but I played around with deploy and using the views plugin I was able to export entities.

The primary issues with content (entities vs configuration) is that content many times needs to be merged from one server to another so it ends up being a fairly complicated proposition.