1. He made his mother surprised.

2. He was surprised at the news.
3. The game was surprising to me.
4. He was surprising his mother at that time.
5. He saw his mother surprising the baby.
(Are they all grammatical?)

All are correct grammatically, but #1 would be smoother if you simply say, "He surprised his mother."

Yes, all five sentences are grammatically correct. The word "surprised" is used as a verb or an adjective in these sentences, depending on its function in the sentence.

1. He made his mother surprised.
In this sentence, "surprised" is used as an adjective to describe the state of the mother. The subject (he) caused his mother to be surprised.

2. He was surprised at the news.
Here, "surprised" is used as an adjective to describe the state of the subject (he). He experienced surprise upon hearing the news.

3. The game was surprising to me.
In this sentence, "surprising" is used as an adjective to describe the game. The game caused surprise to the speaker.

4. He was surprising his mother at that time.
In this sentence, "surprising" is used as a verb in the present participle form. The subject (he) was actively causing surprise to his mother.

5. He saw his mother surprising the baby.
Here, "surprising" is used as a verb in the present participle form. The subject (he) observed his mother actively causing surprise to the baby.

So, all the sentences are grammatically correct, though the use of "surprise" changes depending on its role as a verb or an adjective.