Colleges in Jharkhand

No chance, but you can try for it's Patna campus, maybe you can get CSE there.

Hello Sudhanshu,
You may refer the link below for the list of top engineering colleges in the state of Jharkhand:
https://www.shiksha.com/b-tech/ranking/top-engineering-colleges-in-jharkhand/44-2-112-0-0
this link includes IITs , NITs and GFTIs also.
All the best!

Yes, you can. BIT mesra gives an option to it's students to change branch if there is a seat vacant in the respective branch and you have enough marks to change your branch.

Only the admission in BIT Mesra, main branch at Ranchi is conducted by JoSSA. For the extension centers, you need to visit the particular center and fill their application forms.

Admission procedure for any candidate is same in BIT Mesra, except if you are from a reserved category, then you have to show the category certificate whenever and wherever asked. This certificate will be asked you few times during the admission procedure and you have to produce it positively.
If you want to check the branches you can get admission into use the following:
http://josaa.nic.in/Result2016/result/OpeningClosingRank.aspx

That depends upon whether you are a student from the home state or a candidate from other than home state. You see, there is a reservation for the students who belong to the home state I.e, Jharkhand itself. If you want to lookup the opening and closing ranks for 2016 use this: http://josaa.nic.in/Result2016/result/OpeningClosingRank.aspx