B.Tech Eligibility

Yes, outside students can apply. But you have to give either JEE or GUJCET exam to take admission in here because admission to BE is done on the basis of rank secured in Gujarat Common Entrance Test GUJCET conducted by Gujarat Secondary and Higher Secondary Education Board (GSHSEB) or Joint Entrance Examination (JEE Mains) conducted by Central Board of Secondary Education (CBSE). 60% of JEE marks and 40% of boards marks are taken into consideration for the ranks.

No, it is highly impossible for you to get a free seat at this Rank. You may get into your desired college through management, but with rank>100000 free seat is impossible.

You are eligible for B.Tech courses. Your rank is very good and I think there is some chances of getting good college. Checkout the link below to find the college you are eligible for :
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=6540165.

If you want a good college then you have to qualify JEE Mains but if you didn't take that exam then you can go to the colleges which offer admission without JEE scorecard.

Yes, he is eligible for NEET 2018.

BCA or B.Tech, choose any one of them, if you want to step-in the world of computer education. Your +2 marks is low, so there is probability that you may not get good colleges for B.Tech. But, on this +2 marks, if you are getting a good reputed BCA college, then don't show any hesitation to take admission for BCA. Now, who says BCA is bad? It is a very good and career growing degree. If you join MCA after your BCA, in any of the NIT through NIMCET, then there is no better option than this.