Design

No, you don't need to appear for any entrance exam. You can directly take admission in an institute to pursue web designing course.

Software development is better as compared to web designing. Software designing is a bit challenging and dynamic as requirements of clients vary a lot. Most of the IT companies in India make money by taking development projects.

No you need not visit campus for the entrance test. The test will be conducted in Delhi.

The best fashion designing college in Bangalore is NIFT. Other international schools which you can explore apart from NIFT are The Istituto Marangoni, LISAA (L’Institut Superieur des Arts Appliques). If you want to pursue your UG, opt for the best option available at your disposal.

Dear Jaspreet,
NIFT-Delhi should be on your list as it is ranked one of the best design schools in India. If you cannot make it to the NIFT. I am afraid you don't have many options to choose from. As per me, you explore some international schools who have opened their campus in India. There are few s

You may refer to following link for list of colleges offering Automobile engineering in Chennai: https://www.shiksha.com/top-automobile-engineering-colleges-in-chennai-rankingpage-51-0-0-64-0

You can go for 1 year diploma in any designing course. You can change your track through this.
All the best.