Extend has several meanings, so multiple usages are possible.
To extend something is to stretch it. In this case, it is the time that is allowed for some kind of activity that must take place prior to the event.
The committee has extended the submission period for manuscripts by another week.
Ticket sales have been extended through the week of July 1.
But extend can also mean to push something outward— for example, changing a date to a later date.
They extended the registration deadline to November.
The librarian extended the due date to the 12th.
The cutoff for applications was extended to close-of-business on Tuesday.
In this sense, I wouldn't say it's strictly wrong to speak of a date by itself being extended, but I don't think this usage is typical among native speakers.
The phrase dates extended means that certain events that took place on certain days will now also take place on additional days (for example, a performer having additional shows), and should not be confused.
Due dates are not relaxed. To relax something is to make it less rigid or strict, so one can speak of the rule or requirement that something be completed by a certain date being relaxed, but not the date itself.
The professor relaxed her term paper guidelines; they can now be turned in after the public holiday or by e-mail.