Engineering

Refer the following link:
https://shiksha.com/b-tech/resources/jee-mains-college-predictor

Yes, you can take part in UPSEE MBA counselling 2019.

I suggest you to take the counselling then you will be getting all the information regarding your college career.
https://shiksha.com/b-tech/resources/jee-mains-college-predictor

Yes, you can get admission in Raja Balwant Singh's technical campus for B.Tech but it depends on your interest.

Yes, you can get the government colleges for engineering as you have around 250 marks in JEE Mains based on your percentile. For your reference, I am attaching a link through which you can check for all the government colleges you can get. Check here:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

Yes, you can easily get SGSITS Indore for electrical branch with 13,300 rank because the maximum rank needed for admission here is 50,000. Your rank satisfies the eligibility for this college.

As per my views, history will be better as compared to political science because history can be interesting and political science can get boring sometimes. However, as you said you are in arts stream I doubt you will not be eligible for CSE engineering because PCM is a must condition for the eligibility of CSE.

I am sorry to say but most of the engineering colleges have a minimum cutoff of 60% in PCM so I doubt you will get admission in an engineering college.

The fees is 117k for 3 years.