Think of angular velocity $\omega$, angular acceleration $\alpha$, moment-of-inertia $I$ and torque $\tau$ in the exact same way as you think of normal (translational) velocity $v$, acceleration $a$, inertia (mass) $m$ and force $F$. They have their two equivalent laws combining them:
$$\sum F=ma\qquad , \qquad \sum \tau=I\alpha$$
And you can trust these laws.
If there is a net torque $\sum \tau$, there is an angular acceleration $\alpha$. Regardless of what else is happening at the same time.
Just like, if there is a net force $\sum F$ then there is an (translational) acceleration $a$. Regardless of other simultaneous effects and things.
So for example: If a force pushes at a point on an object that does not cause a torque, or if it causes a balanced torque, then there is zero net torque and no angular acceleration. Whatever angular velocity it has, is not changed. Simple. Other forces might or might not be present - the only important thing is if they cause a net torque.
So, when you ask...
But will the body rotating with constant angular velocity can have zero force
... the answer is yes, a body rotating (constant angular velocity or not) can easily have a net force acting on it, as long as that net force doesn't cause a torque (which it doesn't, if it pushed in the centre-of-mass e.g.).
And when you ask...
if torque is zero that means body rotates with constant angular velocity but is there a force MAINTAINING this constant angular velocity or is it just like inertia in linear motion ?
... the answer is no, there is no need to maintain a constant velocity (rotational or translational) with any force or torque. A motion only requires torque or force to change (and how much torque or force depends on it's inertia), but not to be constant.