It’s fine. Hugo does not care about how you name taxonomies, tags and categories are just conventions. You can call them anything you like.
No. You can have different taxonomies per language version. Therefore if you have a taxonomy called categorias in Spanish you need to define a categories taxonomy in English and assign it in the respective content files manually.
I needed to define the permalinks to get them working.
The only concern is that I translate tags to other taxonomy name (etiquetas) some themes may not work properly.
Some of them seem to have hardcoded references to tags taxonomy in their code.
I am trying Academic now, it seems to work OK when I use custom taxonomies.
But I have seen a tags.html in its layouts directory (layouts\partials\tags.html) that has hardcoded tags taxonomy references in it.
May be it is there for backwards compatibility as it seems to work.
But other themes seem to depend deeply in tags taxonomy with hardcoded values.