CLAT

Books by both Universal and EBC are good.

That is a personal choice and a matter of personal commitment.
In my opinion, you can look at coaching class and for the remainder part self study

Yes, CLAT (in this case) is necessary. It is also imperative to be a top scorer since it is the most sought after NLU.
Do self-study or join a coaching class.

It is best to visit the college or call for confirmation.

It is best to call or visit the college for confirmation.

Please refer to this link:
https://www.shiksha.com/law/resources/clat-college-predictor

CLAT does not require you to have a humanities base, even humanities students will find it completely unrelated. The break up of CLAT is General English, Quantitative Aptitude upto 10th class like pipes, time and distance), etc. , Legal GK, Legal Aptitude and Legal Reasoning. Now you see, CLAT is not inclined towards any stream.

Basically, you want to do law, so you should complete BCA first and then go for a 3-year law course, this way you will have both the degrees.

While one can give CLAT only after 12th, there is no requirement of minimum preparation.

No stream has real advantage in CLAT. Since it is based on GK, Legal aptitude, Logical reasoning, English and Maths. At the most you might have advantage of Maths, but that again is 10th class level. You can prepare on your own or attend coaching classes.