There are controllers that have bluetooth to display stuff on your phone/tablet/etc, if you look in the for sale section here on ES there's at least a few, and probably dozens out there on other sites.
There are also units like the Cycle Analyst from Grin Tech http://ebikes.ca that can display a lot of data like speed, battery usage, distance, etc., and there are things like the Cycle Analogger that work with it that can log all that info including GPS data to a card for later analysis, and possibly output that info to something you could make an app for displaying that on the phone
Regarding speedometers, the controllers/displays have settings for wheel size. They don't usually allow you to enter a specific circumference, just to choose between certain basic bicycle (or scooter) wheel sizes, so for a different type of wheel you might have to pick one that's close, but not quite the same, so the speed and distance measurements will always be off by some amount.
Regarding the display on your existing controller, that 3pin connector looks like it has one of it's wires that goes not to the controller, but to the "integrated" connector. So most likely any display functionality it would have would be provided completely by the scooter or bike that controller was specifically designed for, and so the parts are not available separately.
You could open the controller up and see if the pads the wires all go to are labelled, and then make a list of those, and then look at all the many controller threads here on ES, some of which have some of their pads labelled with functions that have been determined experimentally. Note that just because the abbreviation is the same between two controllers' pads, it doesnt mean the function is the same or works the same way.
It's not all that likely that without knowing what display it was intended to match up with that you'll find one that does work with it, by chance.