Graphic / Web Design

I would suggest you to first focus on your current studies. There is no point in going for a part-time course at this stage. Part-time courses are beneficial to those who have a work experience.

Yes, after BBA if you have an interest in Masters in graphic design, all you need to have is artistic and creative; strong presentation, verbal, visual, and written communication skills.

Graphic design has more scope and offers more opportunities. With the increase in a number of internet users and fast growing e-commerce industry, web/online presence became important for most businesses. Most businesses want to have own website and are looking for skilled web designers.
To be a graphic designer, you need to be creative and you don't necessarily need artistic skills to land a job in graphic design. Also, you need to have knowledge of different languages like HTML, CSS and also have an understanding of Adobe with an entire creative suite including Photoshop, Illustrator, and InDesign.

Yes, go for it. If you are graduate, you are eligible indeed.

Zee Institute of Creative Art
Maya Academy of Advanced Cinematics
Arena Animation
Venture technology are some of the colleges in Ranchi for Web Designing Course.
Also check this to find more colleges:
https://www.shiksha.com/animation/graphic-web-design/colleges/colleges-ranchi?version=2&utm_expid=8943562-14.L3jWz9aOTbmXh4VSK7g4dg.2&utm_referrer=https://www.google.co.in/

For the queries related to the fee and syllabus, kindly get in touch with the college official.
Please refer to the link for details: http://graphiccamp.com/

For pursuing the certification course you need to be 10+2 passed from a recognized board.