internationalization of interface messages in translate extension
For 1) see https://bugzilla.wikimedia.org/show_bug.cgi?id=2085 (the answer is: not by default). For the other parts, I think the answer is also no.
I assume you have already read https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Extension:Translate/Unstructured_element_translation and https://www.mediawiki.org/wiki/Help:Extension:Translate/Page_translation_administration which provide some hints how to handle content translation with what is currently available.
Thanks for the info! For (1) I've found a template [1] that had what I needed, but need to make a landing page to make people able to find their language.
I've read this information yes. I understand that what I asked for is not a part of the Translate extension, just wanted to ask if there is a smooth solution, as you probably have good overview of what is possible to do. My best option now I guess is to make my own drop-down list [2]