Can I say the prayers of Birkot HaShachar and Tikkun Chatzot after Chatzot (Midnight), even if I had not gone to sleep yet? How should I proceed with the Kriat Shema Al Hamitá if I will remain awake after midnight?
Praying it before you sleep or after you sleep will give you the needed blesses from Allah. We call Qiyam before sleeping and Tahajud after sleeping. The best prayer is at the last third of night maybe 2 hours before dawn.
I believe you have the same in Judaism.