3laykum salaam @emreyardimci.
Method 13 uses an older Diyanet calculation so there are differences in timings. Diyanet is not willing to share their new calculation method so there is no actual way to match their calculation, unless we scrape from their website.
Regarding the continuity of the service, it has been running for 12 years, and God willing, will continue to run.
There can, of course, be no guarantees, but the intention is certainly there. You can always get the code from 1x.ax and run the API yourself if you would like to.
InshAllah, I hope this helps.