1. Forgive me. I didn't know that.

Question

2. Excuse me. I didn't see you there.
3. Pardon me. I made a mistake.
(Are they all grammatical, showing 'forgiveness'?)

4. I swear that I will never leave you.
5. I swear to God that he will never leave you.
6. I swear in the name of
God that she will never leave you.
7. I bet he is honest.
Definitely he is honest.
8. I am sure he is honest.
(Are they all grammatical?)

Answer 1

1. Forgive me. I didn't know that.
2. Excuse me. I didn't see you there.
3. Pardon me. I made a mistake.
(Are they all grammatical, showing 'forgiveness'?)

4. I swear that I will never leave you.
5. I swear to God that he will never leave you.
6. I swear in the name of
God that she will never leave you.
7. I bet he is honest.
8. Definitely he is honest.
9. I am sure he is honest.
(Are they all grammatical?)

Answer 2

All are fine.