Format Date from mm-dd-yyyy to dd-mm-yyyy

You can use the function formatDate(datetime value, format).
For example:
formatDate(dtDateTimeVariable,"DD-MM-YYYY")

Alternatively, Nintex uses the Tenant default that your global admin may change (of course this affects everyone everywhere)

More specifically the Tenant default I was referring to is known as "Office 365 sites regional settings".
You can confirm this by going within Nintex for O365 Form Settings-->Regional Settings. You'll see the Region field that indirectly identifies the date and time format.
For example, English (United States) short date is mm/dd/yyyy
Each country/language has a short date format default pre-defined.
So your global admin would need to select the country/language that is appropriate for your organization (and, of course, have previous approval/communication)

I don't have much hands-on with the Classic Designer, however, it looks like the string format expression and "apply formatting to input mode"=Yes look to be appropriate.
Looks like you should open a support case

There is a known bug around the string format on input mode so it does not work. Alswo if it was working there would be no need to use a function. just doing mm/dd/yyy would be enough.
I think setting the format with regional settings is a better idea.

i just tried with just writing the format string and it didnt do the magic. i will have to wait until the admin gives me rights to change it through the regional settings. thanks @SimonMuntz