Question

1. The game was boring to me.
2. He was bored with the game.
3. He saw the teacher boring the children.
4. He saw the students feel bored with the teacher.
5. He made the students bored with the teacher.
(Are they all grammatical?)

Answer 1

no
1. The game was boring for me.
2. He was bored by the game.
5. He was made bored by the teacher

Answer 2

Both you and "priyam" are correct about #s 1-4. In 1 and 2, either of those prepositions can be used.

I disagree with both of you about #5, though. If students are bored by the teacher, "He" didn't make that happen! The teacher did!!

#5 would be better written like this: The teacher bored the whole class.