According to Snell's Law:
$n_1\sin θ_1~=~n_2\sin \theta_2.$
If, $\theta_1 = \theta_2 =~0$
there is no bending but the speed of light changes according to the refractive index.
Is this the case or I am wrong?
There is no bending, but speed of light changes. Your initial statement of Snell's law is wrong, and your angle definition is also wrong. Please try to ask questions that show that you have put in some more work. Basically any textbook would have specifically covered this question.
Edit: you have fixed Snell's Law, but your angle is still wrong.
Edit2: Now you have it all correct. This situation is precisely why Snell's Law needs to be expressed in terms of sine, rather than cosine, say.
Have a think about it. If you are assuming two homogeneous, isotropic media with an interface between them, why would the speed of light depend on which direction the light is travelling in those media?
The speed of light in such media is just $c/n$, where $n$ is the refractive index. Direction does not come into it (though there are more complex media one could consider where it might).