Three issues here.
1. Setting the short and long dates in System Preferences. See fruhulda's answer: Copy and paste to shift the dates position. [Nice one, fruhulda!]
2. Locking those changes in (restart your computer). See Jerry's first answer.
3. However I do not get that window that you show where it saysset to today and gives you those options which you can tick. This has nothing to do with System Preferences. That window is what you get in Pages when you double-click or right-click or Control-click the date object to bring up the options. See Jerry's last answer.
If I could try everyones patience a bit further.
No worries mate.
OK, it is what it is then. Don't delete the spare account. It comes in handy for testing apps.