Not a cross post. It just creates a post that links to the first post.
If you made a third post that also linked to the first post using the same url as the second post, that would be detected and get linked up as a cross-post to the second post.
Actual cross-posts work in both directions. Lemmy detects them as the same thing, both posts link to the other.
Not in the post body, the post body quote and "cross-posted from" text is completely meaningless and just gets added by most clients, adding it doesn't make something a cross-post, and removing it doesn't break the actual cross-post feature, which shows up as a little "cross-posted to: list of communities" thing on the post page.
Thunder has it, Photon does it, and the default webUI does it.