Polytechnic

No, you are not eligible as BBA requires students graduated from 12th standard. If you have pursued Diploma after 12th then you can but if you are pursuing diploma after 10th then you cannot study BBA. Instead, you can get a B.E, B.Tech degree then proceed for MBA.

Yes it's approved.

You can appear for SSC CHSL. It is conducted for 12th pass students. You can also give SSC JE exams after completing Diploma.

The only benefit that you will get is concession in fee. Except for that, there are no other benefits which you will get only in government polytechnic.

With what mode are you pursuing B.Sc. and diploma? If both are regular, then probably your B.Sc. Degree will be invalid or maybe both. Only that degree will be legal where you have given your Migration or Transfer Certificate. You should pursue B.A. Or BBA through distance mode to avoid any legal obstructions later.

Yes, it is approved by AICTE.

Not now. You need a graduation degree to appear for IAS exam. Diploma is not considered equal to a degree. You can, however, pursue B.A. or B.Tech after Diploma and then you will be eligible. You can also pursue a distance course with Diploma.

Not, yet. After completing Diploma or when in the final year then you can apply for Loco Pilot. Before that, you are not eligible.

Here is a list of good colleges in India offering Mining:
https://www.shiksha.com/b-tech/colleges/b-tech-in-mining-engineering-colleges-india.