Information Technology

No, there will be no chance in LNMIIT but you can try for NIRMA. There might be a chance for you to get some branch.

Yes, you are eligible for BCA after your PUC commerce.

Usually, courses like BCA and B.Sc. IT require 12th with Mathematics. Few institutes also enroll just Science students. If you have not studied maths in 12th, then few institutes have provision for it too. You need to checkout the colleges where you are planning to apply. You will get a much better idea then.
All the best.

Microsoft has a lot of courses and resources online. Checkout Microsoft's Virtual Academy (MVA). You can do free courses from them. In order to give certification exams, you need to find a Microsoft test center or vendor near you and get more details. But, if you are planning to learn online then start with MVA.

Visit the below link provided for getting all the details:
https://www.shiksha.com/it-software/colleges/bca-colleges-Mumbai-all.

See, for ethical hacking course, you can do from anywhere in India or from online programs. It's not the big deal if you want to get into this, then I'll prefer you to opt for the B.Tech from CS branch.

From my opinion, you have to opt for MCA.
But after graduation, the best short-term course is
G- CAT master (Graphiti School of Animation)
Duration= 12 months
Eligibility= You should be graduate

Please mention the college where you wish to apply.