Chat and call logs are evidence, not proof. No explanation is necessary. They can consider it, but it will be only 1 small part of the total picture.
It won't hurt to include it.
It's fine to include.
Optional.
The primary evidence would be time spent together. Showing that you lived together for 3 months would be the strongest evidence of a bona fide relationship...much more so than photos, text messages, etc. That stuff is fine to include as well, but don't miss the forest for the trees (aka "you're looking at the small things when the big things are right in front of you").