Coimbatore

Yes, you can join Hindustan College of Arts and Science. It provides B.Sc in visual communication with all the necessary things. This department was established in 1999. The fee status is not in my knowledge.
For more information you may visit the official website of the college.

If you could tell me your rank in the AEEE examination then I may help you easily as the marks cannot predict the ranks, it is a dilemma whether you could get admission or not.

You have good chances of getting almost all the courses like chemical, civil, electronics, electrical, computer science, etc. as you belong to Tamil Nadu, your home state rank has made you eligible for the seat.

The admissions into Amrita University and its other campuses are based on the rank secured in AEEE. They don't consider JEE Mains marks as it is a private deemed university. Score a rank like 4000 to get Amrita University.

Both are really same in all factors. They are highly reputed institutions and offer good education and placements. So, you can prefer any one of these two colleges.
But, PSG Coimbatore is widely preferred to MIT-Chennai, even though both are equal. MIT is Government College, but PSG is a private college.

PSG College of technology, Coimbatore is better than SSN college of Engineering, Chennai. Both come under Anna university affiliation, but the standard of PSG and its reputation is higher than SSN College, Chennai.

Hello Aswanth,
You may refer the links below for the list of colleges that offer M.Sc in food science (technology) in Coimbatore:
1) https://www.shiksha.com/science/colleges/m-sc-food-nutrition-colleges-coimbatore

No, it is not required.