When is the last time one can eat a meal on Motzei Shabbos and still have it considered Melavah Malkah? When is the deadline?
Melavah Malkah means escorting the queen. Therefore the sooner one eats Melavah Malkah the better. However, if one is not capable of eating right after Shabbos one may delay the meal until later, however not later than midnight (Shmiras Shabbos K'Hilchoso 63:5, Yechave Da'as 4:25). Kaf HaChaim 300:14 holds that it should L’Chatchila be eaten within four provisional hours after sunset. I have heard that there were some Chasidishe Rabbis that ate Melava Malkah Sunday morning however I do not know which ones.
One should eat the meal as close to the conclusion of Shabbos as possible. Some rule it should be eaten no later than four hours after Shabbos. Others rule it may be eaten until midnight. Others rule it may be eaten any time throughout the night. Others rule it may even be eaten on Sunday or anytime until Tuesday night, so long as he is making the meal in honor of escorting Shabbos.
 M”B 300/2 and so is evident from sources above that even Torah should not be learned until the meal commences.
 Yesod Veshoresh Havoda 8/12; Kaf Hachaim Falagi 31/59
 Mishneh Berurah in his understanding of Shaareiy Teshuva 300/1; Ben Ish Chaiy Vayeitzei 23
 Chesed Leavraham brought in Ketzos Hashulchan ibid
 Ashel Avraham Butchacher 174