halacha - Can I say the prayers of Birkot HaShachar and Tikkun Chatzot after Chatzot (Midnight), even if I don't sleep yet?

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?