Fan Nickname: The Battle of Belhalla is sometimes 'affectionally' nicknamed 'BBQ Party', since it involves an 'invitation' and something getting burned.
Genealogy of the Holy War has been referred to several times as A Song of Ice and Fire Emblem because of its heavy slant towards political intrigue and morally ambiguous characters. Interestingly enough, the first book was released a scant three months after FE 4.
No Export for You: Pretty much the biggest "gap" in official FE releases at this point. They both have fan translations, but no remakes or anything similar have been announced, and the originals are rather too old for export at this point.
Sigurd/Dierdre and Dierdre/Arvis happen in-game, and Quan/Ethlyn have been married for a while (and have had baby Altena!) before the events of Genaeology. There is also Eldigan and Grahyne, an NPC.
As of Thracia 776, we have confirmed three (sort of pairs): Raquesis' children are Delmud and Nanna - she had her son Delmud by the mercenary Beowulf, and she had her daughter Nanna by the knight Finn. Beowulf presumably passed away either during or after the Battle of Barhara, and it seems that Raquesis thought of her relationship with Beowulf as an affair. The Mitsuki Oosawa manga adaptation plays with this - since Beowulf doesn't exist in that manga, Finn is the father of both children. Finally, Silessa's prince Lewyn and the Pegasus Knight Ferry are also official, and in Thracia, Ferry becomes Silessa's reigning (and much loved) queen. This also confirms that her children, Fee and Ced, respectively have minor and major Forseti blood.
The Luck Stat would be removed from the status screen, but still exist internally, to "create an element of uncertainty."
A journal made by Shouzou Kaga, the series' creator, mentions that he wanted Thracia 776 to be ported to the Nintendo 64 (which probably could've given the game a sales boost since it was the Super Famicom's last game), and for that port, the game's overall difficulty would be reduced so that newbie players could enjoy it.
And for Geneology of the Holy War:
Sigurd started off as a Junior Lord like his son, and Quan started out as a Master Knight, folloing the traditional series convention of Magikarp Power Lord and Crutch Character guardian more closely.
Hilda would have major Fala blood and weild Valflame in the final chapter. Fans speculate she was planned to be Arvis' sister.
Speaking of Arvis, he was going to be the Brainwashed and Crazy foe in the final chapter, rather than Julia. Whether or not that means he could be saved is unknown...
...and apparently, Kaga didn't want Julius to die after his defeat - instead, he'd be freed from Loptyr's control, courtesy of The Power of Love from Julia.
And, perhaps most infamously, Raquesis was actually going to be the mother of Eldigan's son Ares. Also, Vylon was Deirdre's father, not Kurth (kinda makes sense given Kurth looks absolutely nothing like her) which would have made the game's Official Couple incest too. (Unless Vylon was not Sigurd's father at that point, which is definitely possible.) Oh, and Seliph and Julia would automatically become lovers in Chapter 8. Yes, there was actually going to be MORE incest in this game. Altenna and Arion would become auto-lovers too, but thankfully they're Not Blood Siblings, and there were some definite hints of this in the final game as Arion can be made into an NPC if Altena speaks to him in the final Battle.