UPSC

It depends on your interest. If you are interested in engineering then it is a safe option for your future other wise degree doesn't matter in UPSC.

If you get civil in BITS then you should continue to study if you can afford because it has too many scope in future and you can also prepare for UPSC after engineering.

Go for M.A. Public Administration if you are preparing for UPSC CSE.

In UPSC prelims, you need to cover: general studies - History, geography, polity, economics and Science. For CSAT paper 2, aptitude and general mathematics.

There are many government exams to be conducted. 1st SSC CGL last date of form submission 25th November 19, Madhya Pradesh PSC state service exam form submission 20th nov to 9th dec 19. RRB NTPC etc. And UPSC CSE 2020.

UPSC CSE PRELIMS SYLLABUS
Paper 1 - General Studies:
This includes areas like; Indian National Movement, Indian Polity, Basic Economic Understanding, Geography. While these are static part of the syllabus, the dynamic part includes current affairs, General Knowledge and that does not proper definition, thus making the syllabus quite vast. Paper II - Aptitude Test:
Paper II is dynamic in nature and includes mathematics, reasoning, analytical ability, and interpersonal skills. All these areas require spot mental ability.

You can apply 9 times and the maximum age is 35 years as of now.

If you are willing to appear in UPSC CSE rather than IES than this is a different field as IES is technical field but UPSC CSE ask you questions related to social studies, gs and current affairs with Science and maths of 10th level only. So for CSE preparation you must cover ncert of 6th to 12th standard. Then you should move to other books.

UPSC is not an exam it is a government body which conducts various exams like UPSC CSE, UPSC NDA CDS and so on. I can tell you about UPSC CSE. This is a exam for recruiting for Civil servants like IAS IPS and IFS. This is known as one of the toughest exam of world. But by proper strategy and preparation you can get success in that.

Yes, you are eligible as UPSC CSE needs only graduation to appear in its exam and it doesn't matter what the field of graduation is.