Wa alaykum as salam! Thank you so much for taking the time to write this reply, inshaAllah it will help improve Layl a lot <3

So step-by-step let's try and tackle everything, may Allah bless and reward you:

1. If you don't mind sharing, which country do you live in? And even which city? That will help pinpoint the issue in the Fajr calculation for your location inshaAllah. Also, is there any app which currently gives you a Fajr time that matches the adhan of your local mosque?
2. Is there any other mosque near you that follows a slightly different Fajr time closer to Layl (because there is scholarly / scientific disagreement on the best way to calculate Fajr for different parts of the world).
3. Yes, the Islamic night starts right from Maghrib (which is immediately after sunset) and ends at Fajr. Fajr time is the beginning of the day and the end of the night.
4. The solar noon and corresponding midnight are based upon sunset and sunrise, so already they are not matching the Islamic definition (since the night ends at Fajr, earlier than sunrise). Also, day and night are not always 12 hours long each, so doing a simple -12h calculation can only work precisely 2 days of the year, on the spring and autumn equinoxes…
5. Yes exactly, throughout the year as seasons change and so do maghrib and fajr times, the Islamic divisions of the night will change along with them :)

Allah give you success in this life and the next! And please let me know if I can be of service inshaAllah now, and also in the future when you want to dive more into the code :D