Hi,

Yes, you are very much eligible to sit for the UPSC or any other state examination. You just need to pursue graduation in any field from a recognized university. So, by distance education, you can sit for the UPSC and any other state exams as distance courses is also offered by the recognized university only. So, do not worry and prepare for the same. There is no such provision that distance or private candidates cannot appear for the UPSC exam.

Yes,

But why are you doing distance degree? Why not regular while you are planing your future. Suppose that in upsc distance degree is allowed but in future if they changed then what option left for you. You wrote many types of exams. I think you should focus at first. Then think over it. Best of luck.