The ICFAI University, Jharkhand

See, JEE is for testing your knowledge and intelligence depending upon which you can get admissions in NITs, IITs or any other private colleges. It gives a better chance to select your stream and colleges.
But, if you are not interested in giving JEE exam, then you might not get better streams (CS, mechanical, civil, etc.) in govt. institutions at lower rate. You may take admissions in any college but you have to take admission via management quota (which is very expensive)

No, it's a private university.

If mining engineering is there in ICFAI you have to apply for B.Tech (lateral entry) online or offline, application fee rupees 500 enclose necessary documents, applications are screened on basis of diploma marks, if you are selected, you have to appear for interview with original documents (will be returned after verification), the decision of the admission committee will be informed to you after the interview.

The ICFAI University, Jharkhand is recognised by UGC under section 2(f) of UGC Act, 1956 and is empowered by UGC to award degrees under Section 22 of UGC Act, 1956. The University is a member of Association of Indian Universities (AIU). For more information:
http://www.iujharkhand.edu.in/Icfaiuniversity-Jharkhand.html.