Yes. Definitely you can. You can also join diploma after 11nth and 12 th science.

Hi

You can do engineering after your XII even if you had Biology but in some specific streams like Biotechnology, Biosciences, Biomedical, Biochemical, Biological Sciences and Bioengineering. 

You need to check the eligibility for all of these before applying. SRM University and VIT offer such courses. Check their links below: 

SRM - https://engineering.careers360.com/colleges/srm-university-chennai

VIT - https://engineering.careers360.com/colleges/vit-university-vellore

All the best!

Yes you can do the engineering even if you take the Biology in XI and XII class.
The only thing is that you should keep your base strong in the physics chemistry and mathematics,
Because in XI and XII class many of the student choose Biology as there other subject and some of the other students choose computer science as their other subject.

Good luck!!!