Regarding the brocho on the Torah when someone sleeps during the day, as it was discussed dealing with learning Shavuos night. How come we can sleep during the day, taking a nap and the continue learning Torah without making a new brocho. is that not prohibited since one is not allowed to learn Torah without reciting the blessing first?

Shulchan Aruch (O.H. 47: 11) writes that although there is a disagreement between the Poskim, the minhag is not to recite a new blessing for the Torah if one sleeps during the day. Mishna Berura (25) quotes many Poskim that rule that a Brocho on the Torah should be recited and the one who does so does not forfeit. Horav Shlomo Miller’s Shlit’a opinion is that although Poskim do disagree regarding reciting a new blessing for the Torah when one slept more than a half an hour during the day and there is a prohibition of learning Torah before reciting the bracha on it (Mishna Berura 47: 2), Birchas Hatorah is different from other doubtful blessings. The reason being since Poskim do rule that because of the doubt one should not recite the brocho again, thus there is no prohibition of learning then, since that in itself is the ruling of the Torah and indeed it is different from other doubtful brochos such as the blessings on food, when you are not allowed to eat without having recited a certain blessing.