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It is advised that you can join an engineering coaching institute as it increases the probability of qualifying the entrance examination. These institutions provide a proper guidance to the student. They also take periodic tests for the student to assess his strong and weak zones and the student can focus more on his weak zones. Though it isn't mandatory to join those institutes and there are many students who have qualified even without joining any engineering coaching institute, I firmly believe that joining those institutes is recommended. Without the support of those institutes, it will be tougher for a student to qualify in JEE Mains.

You should do B.Tech via lateral entry. Diploma holders in any stream are eligible to take admission, in the second year of the course. They must have done their Diploma after 10th (3-year) with a minimum of 50% or after class 12th (2-year) and they need to qualify LEET. Various engineering colleges in India also offer direct admission to Diploma holders in the second year of the course and in reputed institutes, after completing Diploma, a student gets entry in the second year of B.Tech through LEET. Some private institutes like BITS-Pilani, VIT, LPU University, etc., conduct their separate entrance test.
The best colleges in the north for engineering are:
PEC-Chandigarh
Lovely Professional University
Thapar Institute.

There has been a long-standing misconception that CS/LLB are theoretical courses. Both CS and LLB involve the implementation of laws. Hence, these courses have tremendous practical applicability.
However, apart from key legal aspects revolving around a company, CS also has a lot of routine work. But if you have asked this question with an intention to understand the involvement of 'numbers' in the course, CS has more of it because of subjects like financial management, tax, accounts etc. A CS is expected to be abreast with all areas involved in company's administration, which means an understanding of accounts and financial data is of utmost importance. In that sense, LLB would be more theoretical.
Hope this answers your question.

Basically, don't pick certain courses names and just compare. This is totally wrong logic while doing a career selection. You first be clear as to which one you are more passionate about. Only then you will be able to compare based on passion to choose and zero down on one career. Now coming to the straight answer, all creative segments have great scope. Not just animation or web design but VFX, game design, jewelry design, product design, interior design, UI / UX design etc. Both for the present and for the future, UI / UX designers would be more required. Web designer is only for internet medium. UI / UX designers are for multiple medium and all UI / UX designers have to necessarily know how to develop a website. So a UI / UX designer is also a web designer but a web designer is definitely not UI / UX designer.