Question

1. He is honest in himself.
(Is this sentence grammatical? What is the meaning of 'in himself' then?)

2. He must be angry because she's not saying anything.

3. He has to be angry because she's not saying anything.
(Are both the same and grammatical?)

4. He must have been angry because she were not saying anything.

5. He has to have been angry because she were not saying anything.
(Are both the same and grammatical?)

Answer 1

1 should be "He is honest with himself." (not "in")
It means he's not lying to himself or he is dealing with facts, not hopes and wishes.

2, 3, and 4 are all fine and mean approximately the same thing, but with a tense change in 4.

5 needs to have "she was" in it (not "were" since "she" is singular), and it's fine.