You must distinguish between API versions and application development. As you rightly said, Facebook supports older versions of the Graph API exactly 2 years after the announcement of the successor.
Docs at https://developers.facebook.com/docs/apps/versions#howlong state
The version will no longer be used two years after the release date of the next version.
and
So, if API version 2.0 will be released on April 30, 2014, and API version 2.1 will be released on August 7, 2014, then v2.0 will expire on August 7, 2016, two years after the release of version v2.1.
What happens if you make calls to the Graph API without the specified version information:
The default unversified call will be used for the oldest available version of the API.
means that this application was created on August 1, 2014, you can call v2.0, but not v1.0. If your application was created on April 1, 2014, you can call v1.0 (but only until v1.0 gets installed on April 30, 2015). If your application was created later than August 7, 2014, you can only call v2.1, regardless of what you specify as the version.
This is stated in
An application can make calls to the version of the API that was last available when creating the application, as well as any new, not outdated versions that were launched after the application was created.
Thus, in other words, it was always more relevant at what time your Facebook application was created, because it will determine the version (s) of the Graph API that the application can use
To determine the date the application was created, you can use
/{app_id}?fields=id,creation_time
endpoint, which will give you the Unix timestamp when the corresponding application was created. See https://developers.facebook.com/docs/graph-api/reference/v2.1/app/#readfields Then you can use PHP or JavaScript to convert the Unix timestamp to a date.