What is the ruling on the time between the disappearance of the red twilight and the call to prayer for 'Isha, and is it permissible to pray 'Isha immediately after the twilight disappears and before the call to prayer?

The matter is as you mentioned: the time for Maghrib prayer ends with the disappearance of the red twilight (shafaq), and the time for Isha begins when the time for Maghrib ends, as indicated by the Hadith of Jibreel. Praying it after the disappearance of the twilight is valid. Delaying the prayer until after the twilight disappears is preferable, based on the statement of Abu Barzah Al-Aslami: "He [the Prophet] used to like to delay the Isha prayer, which you call Al-Atamah," and "He used to delay the last Isha prayer until the first third of the night." As for the adhan for it, it should not be delayed beyond the beginning of its time, because it is an announcement of the entry of the time.