Bilvaa Music

Not mandatory to have a basic understanding of Carnatic music to start learning flute, but it will help. However as you start learning and practising flute, you should also get more exposure to Carnatic music by listening to clips, concerts , etc, which will help your learning  process. You can google search for flute bhaskaran , whic is based in Chennai for getting high quality flute lessons in Chennai directly as well as online from any part of the world. Best Wishes for your learning experience 

My recommendation would be to expose the kid to Carnatic music by playing recordings at home and listening along with the kid. For Carnatic music, three years is a bit early for proper Carnatic music lessons. Perhaps five would be comfortable to very few teachers, but seven is OK. If the child is extraordinary -( you will know that quickly or take the child to an experienced teacher for assessment of potential. ), perhaps sporadic cases 3 years could work out. But just being able to sing rhymes and shlokas may not be an indication that you could start so early.
However, constant exposure to good quality Carnatic music (even Indian-style light music or light classical music would be helpful) will go a long way in kidling the child's interest and aptitude. But please continue the classes of shlokas and chants, which will also develop the child's mind and musical / voice-related capabilities. Especially as you have said, there is no family background.
Best Wishes!

It will be useful, but not a must. We have taught people who did not have any background of Carnatic music who have been able to pick up flute playing. They have developed a basic understanding of Carnatic music in the process of learning flute itself. If they are more self-motivated to learn about Carnatic, they can be guided to listen to the various recording, and develop an appreciation.

Rhythm is the heart of drum playing, and a drummer should have rhythm in his skin. That is the way he becomes a master drummer. Mastery of rhythm should be a primary goal for a drummer, in my opinion. This way, the rhythm can even make mediocre music stand out as outstanding music.

The beats add to the overall impact of the music on the listener. Of course in the pure rhythm part of the show, the drummer is the leading performer, and the rhythm aspect is equally if not more, essential to strike the right chord with the listeners and capture a permanent place in their hearts.

Depends - First, the style of guitar you want to learn has to be decided - acoustic, electric or Hawaiian.
Please meet a guitar teacher or school and take a look at guitars and ask him for suggestions, - Do it after this lockdown. Do it on Skype otherwise once you locate an excellent guitar expert. I teach only flute and a bit of vocal, Carnatic. It is my advice.