Hello,

If you mean the date picket, in the frontend search filters, it's using Joomla core calendar picker.
The first day of the week should be automatic depending of the current language detected by Joomla.

About date format, it's too using Joomla core default value, which is the datetime format as saved in database.
I will see later for adding option for this

Note too: i've decided there to be back to the Joomla datetime picker (and not use there the included time picker script still in use for event dates, but not for long) as some work is in process for a new datetime picker in Joomla, which will be really better looking and with "time" option workable (not the case today, with a time picker not easy to use in Joomla core) : github.com/joomla/joomla-cms/pull/11138

Best Regards,
Cyril