Where within prayer is one to recite Birchas Hatorah:
Our custom, as written in the Siddur, is to recite Birchas Hatorah immediately after the morning blessings. The following is the ruling of Admur in the Shulchan Aruch regarding when the blessing is to be said.
Some places have the custom to say the blessing over Torah study right before reciting the Tamid paragraph. Others are accustomed to say it immediately after saying Asher Yatzar and Elokaiy Neshama, (or after Hagomel chassadim Tovim and the Yehi Ratzon). This is the more proper custom to follow [and so is the Nussach of the Siddur to say Birchas Hatorah after the Yehi Ratzon which concludes Birchas Hashachar].
Selichos: On days which selichos is recited one is to say the blessing of Birchas Hatorah prior to Selichos.
 They are not concerned with the recital of the Torah verses which are said in the prayers before the Tamid, prior to saying Birchas Hatorah, as these verses are being said as a supplication and not as a form of learning or reading of the Torah. [ibid]
 The reason they do so is in order to precede the blessing over Torah study to the recital of any verses of Torah which are said as part of Karbanos. [ibid] However according to all there is no prohibition in praying to G-d and saying blessings prior to reciting the blessing over Torah study. Thus there is no need to precede the Torah study blessing to the other morning blessings. [Shaar Hakolel 1/16]
 So is written also in Siddur Rav Amram Gaon ; Rambam; Tanya RabasiAbudarahm; Seder Hayom