1) Who is Scáthach?
Scáthach is the warrior woman who varyingly lives in the 'east of the world' who Cú Chulainn is sent to train with:
Then Domnall said that Cuchulind would not have profession of
instruction until he came to Scathach, who was in the east of Alba. So
the three of them went across Alba, viz. Cuchulind, and Conchobar, the
king of Emain, and Loegaire the Victorious. [Tochmarc Emire, Rawlinson
B. 512, Trans. Kuno Meyer]
« Is there in the world a woman-knight who is better than the
woman-knight with whom I am now? » asks Cuchulainn. « There is »,
answers the big man : « for Scáthach daughter of Buanuinne, king of
Scythia, in the east of the world, is better than she. » [Do Fogluim
Chonculainn Annso Sios, Egerton 106, Trans. Whitley Stokes]
Her training is seemingly famous and well known
Then four Irishmen who were in the steading to be trained came to him,
and gave him many kisses, and were asking him news of their own
country and land ; and he asked them news in the same way. « Well, O
vouths », says Cuchulainn, « what training in feats of valour and
warfare have ye got in the year ? » « We have got », they answer, «
the Bridge of the Leaps. » « How long were ye learning it ? » asks
Cuchulainn. « A training of a quarter and a month and a year and
three days and three nights. » « Well then, O youths », says
Cuchulainn, « will ye give me guidance to it ? » « Alas, O boy »,
they say, « what profit were that to thee until Scáthach comes to
teach thyself like every one else ? » « I wish to see it », saith he.
[Do Fogluim Chonculainn Annso Sios, Egerton 106, Trans. Whitley
Then they bade farewell to Scáthach, and paid the fees for their
training by her ; and tidings of them are not told till they reached
the country of the men of Catt. [Do Fogluim Chonculainn Annso Sios,
Egerton 106, Trans. Whitley Stokes]
2) Who is Aoife?
Aoife is another warrior woman who Scáthach seems to have an ongoing feud with:
At that time also Scathach had a feud against other tribes, over whom
was the princess Aife.
... she was afraid of Aiffe, because she was the hardest woman-warrior
in the world. [Tochmarc Emire, Rawlinson B. 512, Trans. Kuno
Cú defeats her in combat and trades her life for three wishes:
Then they fought upon the path, Cuchulind and Aiffe. Then she broke
Cuchulind's weapon so that his sword was no longer than its hilt. Then
Cuchulind said : « Woe is me ! » said he, « Aiffe's charioteer and her
two chariot-horses have fallen dovvn the glen, and all have perished.
» At that Aiffe looked up. At that Cuchulind approached her, seized
her under her breast, threw her across (his shoulder) like a burden,
and went to his own host.
... « Life for life ! » she said. « My three wishes to me ! » said
he. « Thou shalt have them. » « These are my three wishes : thou to
give hostages to Scathach without ever again opposing her, to be with
me this night before thy own dun, and to bear me a son. »
It is granted thus and was all done. Then she said she was pregnant.
She also said that it was a son she would bear, and that the boy would
come to Erin that day seven year. And he left a name for him.
[Tochmarc Emire, Rawlinson B. 512, Trans. Kuno Meyer]
Aoife being Scáthach's sister seems to only be found in one translation of a text, I've only found it in Kuno Meyers translation of Aided Óenfhir Aífe 'The death of Aífe's only son (lit. Violent death [of] One-Man [of] Aífe)' where we see the two lines:
.. Scathach Uanaind, daughter of Ardgeimm, in Letha, until he attained
mastership of feats with her. And Aife, daughter of Ardgeimm ... [Aided Óenfhir Aífe, Yellow Book of Lecan, Tans. Kuno Meyer]
I haven't found this connection in any other text.
3) Who is the un-named brother?
Scáthach has plenty of children (that Cú kills) and family, but I can't find any brother, there could be one referenced in other texts, but none I've looked at.
- Tochmarc Emire, Rawlinson B. 512, Trans. Kuno Meyer
- Do Fogluim Chonculainn Annso Sios, Egerton 106, Trans. Whitley Stokes
- Aided Óenfhir Aífe, Yellow Book of Lecan, Tans. Kuno Meyer