Riddle 1:
> "The first night of the feast I will tell you all,
> But the second night I will show you the way."
Answer: The Mirror of Erised.
The mirror reveals your deepest desire. On the first night, it shows Harry his parents, fulfilling his desire to see them again. On the second night, Dumbledore (representing "the way") shows Harry the mirror.
Riddle 2:
> "I am the one who is not to be named,
> I am the one who is the enemy of the one who is to be loved.
> I am the one who is the greatest danger of all."
Answer: Voldemort
This riddle, while not overtly stated, points to Voldemort as the main threat. It emphasizes the connection between Voldemort (the one not to be named), Harry (the one to be loved), and the danger Voldemort represents.
Riddle 3:
> "I am the key, but I am not to be used.
> I am the one who opens and who closes.
> I am the one who is always searching for, but who can never be found.
> I am the one who is the answer. "
Answer: The Sorcerer's Stone
The riddle describes the stone's role. It is the key to immortality (not to be used, as it is dangerous), it opens the possibility of defeating Voldemort and closes the threat of his return, it is what everyone is searching for, and it holds the answer to defeating Voldemort.
Let me know if you'd like more clarification on any of the riddles!