Regarding the second part of your question:
How is $PQ = OP* \Delta \theta$ ?
The author is probably assuming that the angle $\Delta \theta$ is very small. In that case as you see in the following image (where the angle is denoted as $\theta$, the $\sin\theta$ is approximately equal to the arc.
The arc length is equal to $R\cdot\theta $, where R is the radius (which is equal to one for this cycle. So you end up having (in the general case) that $R \sin\theta \approx R\theta\Rightarrow \sin\theta \approx \theta$ (where $\theta$ is in radian.
Now, in your case, like you noticed, $PQ$ should be given by
$$PQ= OP\sin\Delta \theta$$
However for an infinitesimally small $\Delta \theta$ you can use the small angle approximation $ \sin\Delta\theta \approx \Delta\theta$ and the above results in:
$$PQ= OP\cdot \Delta \theta$$
Unfortunately regarding the first part, I could not understand exactly what you were asking. I would be glad to update the question if it becomes clearer what is point 1 and point 2, and what is it that you don't understand.
Regarding the first part there is still ambiguity. I will try to reply to what I understand :
It says $V\sin\alpha$ ( component of velocity perpendicular to OP) is the cause of angular displacement.How is it ?
if only $V\cos\alpha$ existed we need not turn over head to always to look at a particle. What does this mean ?
It's easier to reply about $V\cos\alpha$. If you see in your image, $V\cos\alpha$ is parallel to $OP$. The observer is standing on O. If only $V\cos\alpha$ existed then the observer would only see the object to travel either away or towards the observer (point O).
Regarding the other part $V\sin\alpha$, $V$ can be decomposed in many way. One way is as $V\sin\alpha$ and $V\cos\alpha$. $V\sin\alpha$ is perpendicular to $V\cos\alpha$. So $V\sin\alpha$ would make the observer at O rotate his head in order to follow the object at P.
Also , Can we say that V is the linear speed ? Because that is the one tangential in direction.in
I am not sure what you ask with "V is the linear speed?". Velocity is a vector and always point to one direction. It is always tangential to the trajectory of an object when its moving (this is a consequence of velocity being the rate of change of displacement).