BCA

You should have secured a minimum aggregate of 70% to stand eligible for the BCA programme.

Yes, you can do it.

I would suggest you to rethink on your decision. What makes you interested in Political Science after BCA. I feel, you should think about getting employable rather than getting qualifications. Still if you wish to diversify, then go for M.A. Political Science directly based on BCA.

Yes, you can opt for BCA, however I would suggest BE in Computers instead of BCA.

The following are the best Colleges of BCA course in Pune.
1, Bharati Vidyapeeth Deemed University
2. St. Mira College for Girls BBA Computer application)
3. Savitribai Phule Pune University
4. MITWPU.

The following are the few Colleges offering the BCA+MCA dual degree course in Madhya Pradesh.
1. Renaissance University Indore
2. IIPS Indore.

The eligibility criteria and admission details related to BCA of Symbiosis Institute of Computer Studies and Research, Pune are given below.
Eligibility criteria : Student passing XII from any stream or equivalent government approved diploma in Engineering/Technology with minimum 50% marks (45% for SC/ST candidates)
SELECTION PROCEDURE : Symbiosis Entrance Test Score, Personal Interaction and Writing Ability Test (PI-WAT)
So from above you are eligible. If you have completed you Engineering Diploma with minimum 50% of marks.

Yes, you are eligible for BCA from St. Xavier College, Ahemdabad. For more details click on the link below.
Good luck.