Science

The course offered is B.Ed and B.Ed in special education. The duration of the course is 2 years.

No, you can't you have to give the exam for hotel management again NCHMCT and clear it. You cannot have a Diploma degree and join B.Sc course as second year.

Yes, but both entrance test will be held on the same day, one is at 12:00 noon and other one is at 3:00 pm on 28/05/2019.

These subjects are under the General Ability Test (GAT).
You can get the previous year's papers on Shiksha's link below
https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/exams/amp/nda/question-papers&ved=2ahUKEwjQz9LFk-7gAhVLRo8KHdQaBm0QFjADegQIAxAB&usg=AOvVaw03ak-lq0rSN2jqs0O92jEq&cf=1.

Candidates from other recognised universities are considered for admission into PG Arts and Science
courses only if they possess a three year Bachelor Degree of 10+2+3 or 12+3 or 11+1+3 pattern, with the prescribed minimum percentage of marks, unless otherwise specified. Candidates who acquired Bachelor
Degree by Distance Education without 10+2+3 pattern are also eligible for admission into P. G. Courses, subject to submission of residence certificate. Because distance degrees are permitted here. So, you can apply.
Good Luck.

Biotechnology will have lots of scope and opportunities in the coming years, it is an emerging branch for the students who are interested in Biology and cannot afford a doctor's degree. It will have a duration of four years like any other branch of engineering. But, I would suggest you to do it from any good and reputed institute, as that will also matter a lot.
All the best.