Exam

Yes, you can get admission in a govt. engineering college like Govt. Engineering College, Kannauj.

For B.Design programme, there is no mandatory requirement of Mathematics but for B.F.Tech programme, candidates should have passed in 10+2 qualifying examination with Physics, Chemistry and Mathematics as main subjects from a recognised state or national board of education.

Candidates should have passed in 10+2 qualifying examination from a recognised state or national board of education.
Candidates passed from public University/ School/ Board examination in India or foreign countries must be recognised under Association of Indian Universities as per 10+2 pattern of edu

You can opt for physics, zoology or botany honors. Since zoology, botany and physics can be taken as optional subjects while preparing for UPSC because physics is a common subject.

No, you cannot get admission in OU with this rank.

Yes, you can as you have scored well.

Which group did you opt for in class 12th, PCM or PCB?

Yes, many colleges allow that. I don't think it would be a problem.
Good luck.