BCA

Yes, it is good in comparison to other colleges offering this course.

Following are the best colleges in Lucknow -
1. University of Lucknow
2. IMRT
3. SRMU
4. AMITY
5. BBDU.

You can start learning everything from Scratch. Just know the logic behind programming and the Syntax of all the programming languages. Basically, you will face a lot of problems initially, but once you get used to programming it will be easy.

The eligibility criteria for most of the colleges for these courses are passing with 50% aggregate marks in 10+2. (Some colleges may ask for Maths as a subject in your 10+2).

No, because BCA is a UG course. And unfortunately, JNU conducts only PG courses now. You can do courses like MCA and M.Sc etc. from JNU, but only after completing your UG course.
Still, if you want to study a UG course from JNU, you must choose any foreign languages, because Jawaharlal Nehru University offers UG courses only in foreign languages right now. These UG courses include BA (Hons) in French, German, Korean, Persian, Arabic, Pashto, Chinese, Japanese, Russian and Spanish. Hope this helps!

Yes, It is one of the famous college. According to me, this college is good

BCA fee structure differ according to colleges or universities so please specify for which college you are enquiring after that we can only help you basic fee structure is INR. 1.5 Lacsto INR to 6 Lacs INR for three years, if you crack any good college entrance exam then you can do by less fee with the help of scholarship etc.

As there are many colleges in Maharashtra, I would suggest you that go for degrees from Pune University, as their degree are highly ranked in any of the state or abroad as well so go for it. And, also in Pune there are many top ranked colleges.

Some colleges will not have any problem if you studied maths in 12th or not for BCA course, but some colleges have the eligibility, criteria that student must have taken maths in class 12th. Therefore, it depends on the college you are applying for the course. Once you get admission in BCA you can then surely give NIMCET exam for MCA course in NITs.