Until what time may one recite Birchas Hatorah?

If one did not Daven Shacharis or Maariv then Birchas Hatorah may be recited up until the time one goes to sleep.[1] It is forbidden to learn Torah until he says Birchas Hatorah. This applies even if he remembered at night [prior to Maariv]. After awakening the next morning from a standard sleep he is to repeat the blessing as usual, even though it was recited a number of hours earlier at night. If however one already Davened Shacharis or Maariv, then the blessing is not to be said.

May an Onen recite Birchas Hatorah after the Kevurah?[2]

Yes. If he is still able to Daven Shacharis it is to be recited prior to Shacharis.[3]

The Kevurah was at night:[4] He is to recite Birchas Hatorah prior to Maariv. After awakening the next morning from a standard sleep he is to repeat the blessing as usual, even though it was recited a number of hours earlier at night.

_________________________________________________________

[1] As it is forbidden to learn prior to the blessing, and there is no reason or source to say that the blessing may not be said at night, even according to the Iggur. See Admur 47:7 that the blessing is said at night, and see Dvar Moshe 3 Y.D. 13

[2] Dvar Moshe 3 Y.D. 13; Shaareiy Teshuvah 71:1; Shalmei Tzibur p. 182; Ashel Avraham Butchach 71; Kitzur SHU”A 196:7; M”B 71:4; DErech Hachaim; Kaf Hachaim 71:4; Nitei Gavriel 18:21

[3] Dvar Moshe ibid, based on the above Halacha

[4] See Dvar Moshe ibid; Upashut that there is no reason to differentiate between whetehr the Kevurah was by day or at night and either way he is obligated in the Mitzvah.