Question

1. I don't read the novel yet.
2. I cannot start to do the work yet.
3. I will not open the bottle yet.
4. I don't want to go there yet.
-------------
Are they all grammatical?

Answer 1

1. I don't read the novel yet.
2. I cannot start to do the work yet.
3. I will not open the bottle yet.
4. I don't want to go there yet.

5. I didn't read the novel yet.
6. I couldn't start to do the work yet.
7. I would not open the bottle yet.
8. I didn't want to go there yet.
-------------
Are they all grammatical?

Answer 2

#1 is incorrect; #5 is a bit awkward; all the others are fine.

To correct #1, you'd write, "I haven't read the novel yet."

#5 would be much better if you omitted "yet."