The characters for Fujiwara literally mean "Wisteria field", and Mokou "Scarlet (younger) Sister". According to ZUN, however, Mokou can also mean "Paint me red" and her name has no connection to Flandre Scarlet. In the right context, 'Kou' can also be translated as 'female phoenix bird', which is fitting, while 'Mo' can be translated as 'mourning' Her name would mean something similar to 'Mourning female Phoenix bird', a name somewhat fitting for her exiled life and events of her past.
Considering Mokou's surname and her back story as a daughter of an aristocrat charmed by the Kaguya-hime of legend, she is supposed to be the daughter of Kuramochi no Miko (車持皇子), who was given the quest for the Jeweled Branch of Hourai by Kaguya. His model is speculated to be Fujiwara no Fuhito, the factual founder of the Fujiwara clan, a powerful clan of regents during the 9th to 13th centuries.
Another note is at that time it was common for aristocrats to have "の" (pronounced no) between their surname and first name or their title and name. Thus the English equivalent of her name would be "Mokou of the Fujiwara Clan".
Mokou appears on the cover of Imperishable Night, silhouetted against the moon beneath the silhouette of Kaguya.
The paper talismans on Mokou's pants and hair ribbons might be wards to protect them against being burned by fire. Her shirt, which lacks those talismans, appears to have been burnt repeatedly, while the ribbons and pants show no such wear.
Because Mokou can't die, there are some parts of Gensokyo she cannot visit, such as Hakugyokurou. This is because being in the netherworld is equivalent to being dead, as quoted by Yuyuko in Perfect Cherry Blossom, and by Mokou in her confrontation with Yuyuko.
The fact it took the combined efforts of her, Kaguya, and several rabbits to put out a forest fire in her Bohemian Archive article implies that while she's capable of starting and increasing fire, she might not necessarily be able to extinguish it.
In Cage in Lunatic Runagate, she is shown as having had short, dark hair when she was mortal. No official explanation of this is given, though this could be due to her hair greying, due to her old age, and not cutting it.
She seems to have a good relationship with the members of Eientei despite her feud with Kaguya and is willing to lead the rabbits home. She also seems to have a good relationship with Keine Kamishirasawa.
In Canon, the Spellcard 199 in Imperishable Night might refer to Iwakasa, as she implied she felt regret over causing his death.
In the same Chapter in Cage in Lunatic Runagate: Chapter 4, it is shown that her immortality was derived indirectly from Iwakasa as well, as he saved her life prior to her immortality.
Mokou was planned to be a playable character in Touhou Hisoutensoku, but was scrapped due to a lack of time to balance her move set; ZUN stated in an interview she would have been overpowered and would unbalance the game (the same problem was encountered with plans to add Kaguya to the playable roster as well).