Question: Can we pray the Mode Ani in bed or should we first be dressed?
Answer: Yes the Mode Ani can be said in bed at the moment of awakening.
Question: There are certain prayers such as Tikkun Chatzot, and Perek Shirah by King David. Are Noahides permitted to say these, and if so, may the rabbi please give guidelines on how to say them and relate to them?
Answer: Tikkun Chatzot and Perek Shirah should not be said by Noahides as they are not related directly to the 7 commandments. Most of the Jewish people even among the observant Jews are not saying it. On the other hand, Psalms can be recited with no limitations.