1. Would you say hi to your mother?

2. Would you say hello to your mother?

(Are both interchangable? Are both the same?)

3. He is also a good cook.
4. He can also cook well.
5. He also cooks well.
6. Also he can cook well.
7. He can cook well also.

(Are they all grammatical? Would you check the position of 'also'?)

1 and 2 are about the same and are interchangeable, yes.

3 - 7
All are fine. The position of 'also' affects the tone of the sentence and sometimes what the sentence implies.