If one goes to sleep, wakes up for Tikkun Chatzot and learning of Mishnayot and other texts, what is the halacha regarding: 1) negelvasser when one wakes up both in the middle of the night, and when one wakes up later, (according to both the G"ra who says the ’Al Netilat Yadayim is for Tefillat Shacharit, and other opinions) with a Bracha. 2) the Bircot Hatorah, which are required before the Psukim in the Tikkun as well as the learning, but what is the Halacha regarding when you go back to sleep and then wake up later? should one be Yotze through someone else? lastly, if someone does not sleep for Shnat Keva before waking up for Tikkun Chatzot, do the same Halachot apply?
For Netilat Yadayim: If you wake up for the first time before Chatzot, you should wash without a Brachah (there is a Machloket KH”C GRA”Z and Safek Brachot Lahakel) and then again with a Brachah after you wake up second time for Shacharit. If you wake up for Tikun Chatzot after Chatzot, two valid opinions are found by the late Halachic authorities; therefore you can either wash first time with a Brachah or the second with a Brachah. (See Pninei Halacha - Tfilah) For Birkat Hatorah: You should say the Brachah twice, after both the first and second awakening. (MB 47; 29) A short nap less than 60 breaths is not Halachacly a sleep. (Shulchan Aruch OC 4; 16. Biur Halachh ibid.)