Rajasingan

In my opinion, both types can help you sing film music better.  You may choose anyone and also learn light music simultaneously.

I would also recommend you go through Youtube videos of difference between carnatic vocal and hindustani vocal to get better understanding. 

It all depends on your inborn and grasping ability. Some people will learn in less than two months, while some people take more time. 

My personal advice is don't worry about the time or duration. Just attend class and start practicing. All the best! Contact me personally, if you want more help in this regard.

Learning Carnatic vocal first can be a great advantage. I usually recommend the beginners to learn any form of vocal music (Carnatic, Hindustani, even light music) before trying to play any instrument.

Learning vocal music helps to improve your musical wisdom, which will allow you easily grasp the tunes and raaga through listening.

The answer can be both "yes" and "no".

Some people will find learning carnatic easier, while some find difficult.

Generally, people from South India, who have more exposure to Hindu devotional songs, bhajans will find it easier to learn Carnatic than people from north India or foreign country.

So, don't come to conclusion. Find a good teacher and he will be able to guide you in this regard.

Thanks