I added the missing translations for the lightbox in UX: Add translations for lightbox · discourse/discourse@7e8579b · GitHub.
The “Insert date” dialog should already be fully translatable.
This was fixed in New user of the month: wrong month, not localized - #5 by gerhard.
Regarding the "YYYY-MM-DD` date format: As far as I can see our datepicker always uses that format. Changing that behavior so that it shows a localized date while making sure that nothing breaks will take a little bit more time. I’ll take another look at this at a later time.