The date shortcode pulls the date from a php function - to remove the "th" part of the date for example you could use a custom function like this:

Install this plugin

and add this this code snippet to it.

function newdate_displaydate() {
    return date( 'j F Y' );
add_shortcode( 'newdate', 'newdate_displaydate' );

Then in the widget itself (Appearance > Widgets > 'Top Toolbar - Right') change the shortcode from [date] to [newdate]

That will display the date without the "th".

To view all the different options you have on formatting the date string see this guide:

If you need to do additional translations of the month name etc - this would need your server to return the month value in your language - you would need to talk to your web host about that.