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If you want to do MBA, I would suggest you to go for full-time MBA because that will provide you more job opportunities in future.

You need to move ahead according to the instructions, but in most of the cases, you don't need to do that.

Yes, you have to apply for VITEEE exam then only you can get admission into college for B.Tech and M.Tech integrated course.
For more details visit the link provided:- https://www.shiksha.com/b-tech/course/integrated-b-tech-m-tech-in-software-engineering-vit-university-vellore-chennai-campus-vandalur-243304.

CLAT, AILET and ISAT are conducted for the admission of law programme in the central universities. CLAT registration is closed now since the date was only 31 March 2018 but you can register for remaining two exams. For AILET the date of closing is 14 April and for the ISAT exam the closing date is 4 May 2018. Many private UNIVERISTIY conducted their own entrance exam for the admission in the law programme. So for this you have to check k on your own in the official website of the colleges for admission

Which NET are you are talking about?

No, not the demand draft but you'll have to mail the certificates.

For your complete SVUCET query, check out the link attached below:
https://www.google.co.in/amp/s/www.shiksha.com/university/sri-venkateswara-university/exams/amp/svucet.

The last date of submitting MHCET Law application form for five-year integrated programmes was March 30, 2018.