To answer your first question - No you can not enter the course of B.Tech Biotech without maths in your +2. B.Tech is an engineering course and therefore any entrance exam will require you to have maths. First you need to clear the exam, only then do you get the option of choosing biotech. Both IIT and VIT entrances require maths even for joining B.Tech Biotech course.
2. You can join B.Sc Biotech course in almost all colleges of the country with your current subjects.
3. Is B.Sc better or B.Tech? That is subjective depending on your interests and where you plan to do your course from. Majority of students who pursue B.Tech biotech get placed in IT companies and do jobs that are not in the least related to their field. In case your aim is to enter research in the field of biotechnology, then further studies are necessary.
4. If you have decided that you want to pursue post graduation then you have 4 options -
a) B.Sc (3y) + M.Sc (2y) + PhD (3-7y*)
b) B.Tech (4y) + M.Tech (2y) + PhD (3-7y*)
c) B.Tech (4y) + PhD(3-7y*) (very rarely only brilliant students are allowed this option)
d) B.Sc (3y) + M.Sc(2y) + M.Tech(2y) + PhD*
You can stop at any phase during any of these options.
* There is no limit to the time period taken to complete a PhD. It all depends on how nice your PhD guide is in the end.
5. What kind of field within biotech are you interested in? Does bioengineering intrigue you? Designing biomaterials etc? In that case you will learn more and get more opportunities in a B.Tech course. Else do you like molecular biology? Genetic engineering? cell biology? This field is usually covered in the B.Sc/M.Sc courses.
6. Starting package? That depends purely on what field you decide to enter. If you enter research or get a Ph.D position and manage to secure a fellowship after M.Sc then you can expect INR 25,000 for the first 2 years following which it increases to INR28,000 for the next 3 years of Ph.D (after 5 years into Ph.D you stop receiving fellowship)
If you want to get into the private sector, then payscales vary from company to company but they are definitely not more than what a researcher gets. If you decide to go out of the country for further studies, then you can manage to get scholarships and fellowships that are comparatively much higher.
Some of the good colleges for B.Tech include IITs, VIT, Thappar, SASTRA, NIT etc.
Good colleges for B.Sc Biotech include Fergusson College, Pune University, BVP Pune, various colleges in Mumbai university amongst others.