B.Sc

You can become a teacher or you can become a researcher in anthropologist survey of India. You can also go for WHO, UNESCO, and UNICEF.

For B.Tech, you need to give EAMCET. For B.Sc, AUCET should do.

Yes, It is indeed possible. It is offered by BITS-Pilani. Since, BCA is a 3-year degree programme, the duration of M.Tech course is 4 years (for B.Tech/BE students, it is 2 years). BITS-Pilani has a separate division called WILP (Work integrated learning programmes), wherein working professionals can continue their higher studies. Wipro offers its candidates M.Tech through WILP BITS-Pilani. Students work on live projects from Monday to Friday, attend M.Tech classes on Saturday and have their semester exams also conducted on Saturday/Sunday.

Yes there are colleges offering integrated B.sc and B.ed courses - Sharda University, Indian Institute of Teacher Institute, Regional Institute of Education, Bhopal/Bhubaneswar
Lovely Professional University
Chandigarh University
G.D.Goenka University
Arunachal University

Tezpur University is really a good university and has earned the recognition from all over the country. To crack TUEE, you just need to get your NCERT basics clear and sorted. After that practise some questions from the previous year papers of Assam CEE and you are good to go. The difficulty level of the paper is not much, it's the limited number of seats that offer massive competition. As for the 2nd part of the question, there is IIT Guwahati and NIT Silchar which can offer you your recommended course but I am not sure whether it is an integrated one or not. Hope this helped!