1. She looks happy.

Question

2. She looks like a professor.
3. She looks like she is a professor.
[Are they all grammatical?]

Answer 1

1. She looks happy.
2. She looks like a professor.
3. She looks like she is a professor.
4. She looks as she is a professor.
5. She looks as if she is a professor.
6. She looks as if she were a professor.
7. She looks as if she was a professor.
[Are they all grammatical?]

Answer 2

These are correct: 1, 2, 6.
Sometimes 5 is used.