Hi!
Thanks a lot for the bug report.
the permalink can’t be edited when editing an existing post. In the beta 3 also (i didn’t test the previous beta versions)
This should be fixed in 1.7beta5 that I just uploaded.
Everything looks ok.
I never tested “duplicate post” but everything does not look ok. Polylang has never been able to accept more than one post per language in a translation group. So my guess is that by duplicating ‘aaa’, you broke the link between ‘aaa’ and ‘bbb’ to create a link between ‘copy – aaa’ and ‘bbb’ (as shown in the second picture). But
‘aaa’ stills contain a wrong information as Polylang is not aware of what “duplicate post” does and thus did not update ‘aaa’.
For a better comprehension, are you starting with Polylang with the beta or were you already using the previous versions? Indeed, old versions of Polylang reset the translation group when changing a post language in quick edit. This is no more the case in v1.7 when the new language is free in the translation group. So I guess that you should have break all the links if you attempted the same thing in v1.6.5. Could you confirm?