Yes , One should  apply for every college where they want to be because taking an admission is the decision that you have to take once you are qualified for those college. So better fill both the forms , focus on exams and then decide where you should go.

YEs you can. However, the procedure is like this. You need to register once since both courses belong under engineering.

The brochure says -A candidate can select and fill as many courses as he wants in the same form, whenever he/she wants , if all the selected courses belongs to a single exam category . In this case it is Engineering

Once you fill the details and submit, you will have to pay Rs 1000 for the course which may be B.Tech here. Then to apply for B.Tech Biotechnology, you should login using your login id/password. Then go to the Course details tab and can apply for B.Tech Biotechnology in the same way.