Content translation of paragraphs
Yes, that API doesn't support passing in the language.

I would recommend you use a view mode for what you are doing. You can click that together in the UI, configure the fields you want to see there and then just call $node->view('your_view_mode'). That should just work.

You could also use the Entity View block provided by ctools module, then you can place your sidebar as a block in a region and don't need any custom code at all.