Must one learn Torah immediately after reciting the blessing?
It is proper to beware to learn Torah immediately after reciting Birchas Hatorah and not to make any interval between the blessing and the learning. For this reason the custom is to recite the verses of Birchas Kohanim immediately after reciting the blessings over Torah. [One is thus not to delay at all the saying of Birchas Kohanim after Birchas Hatorah. If one made an interval between the blessing and the learning, he has nevertheless fulfilled his obligation and the blessing is not to be repeated.]
 47/7; Michaber 47/9; Levush; M”A 47/7; Kaf Hachaim 47/19-20
Admur ibid records a dispute regarding whether one must learn Torah immediately following the blessing or not:
Lenient opinion: Some opinions [Tosafus Brachos 11b] rule one is not required to learn immediately after the blessing and rather even if he made an interval between the blessing and learning it is considered as if he made this interval in the midst of his learning, which is not considered an interval, as will be explained. This is not similar to the blessings over Mitzvos and Birchas Hanehnin in which case if one were to make an interval between the blessing and the beginning of its action he is required to repeat the blessing. The reason for this is because by the latter blessings [Birchas Hamitzvos; Birchas Hanehnin] it is not obligatory to do the action [i.e. eat the fruit] at the specific time that its blessing was recited, as the food could be eaten at a later time if he so desires. Therefore if one makes an interval between the blessing and its action it appears that the blessing is not being said in relation to that action that was done. However by the Mitzvah of learning Torah which is a constant obligation, when one makes an interval between the blessing and the learning, it is not considered an interval being that one is required to learn Torah even during the time that the interval was made. Stringent opinion: However there are opinions [Rosh Brachos 13; Rashal; Darkie Moshe; Bach] which argue on this [and do not differentiate between the two types of actions, and thus one must always do the action immediately after the blessing, even in a case that the action is a constant obligation to be done].
Final Ruling: It is proper for one to be stringent. Thus one should be careful to learn immediately following the blessing. [Nevertheless the main Halachic ruling follows the first opinion. This is implied from the fact that Admur is plainly rules like this opinion and only brings the dissenting opinion as an alternative opinion, and rules that it is only proper, not obligatory to be stringent like their view.]
 As we mainly rule like the opinion which does not require one to learn immediately afterwards, and thus in their opinion saying another blessing would be a blessing in vain. [so is implied from Admur ibid and so concludes Mateh Yehuda 47/14; Kaf Hachaim 47/19; M”B 47/19]
Other Opinions: The following Poskim rule that the blessing is to be repeated: Bach; Peri Chadash 47/7; Chayeh Adam 9/4.
Should one hear the blessing from another person? The M”B ibid rules that one is to hear the blessing from another person or fulfill his obligation in Ahavas Olam. However from Michaber and Admur ibid it is implied that one is not required to hear the blessing from another.