Science

Yes, you can, but you need to justify such a long gap. I would suggest you get in touch with the admission counsellor of the respective college before taking admission.

It's better to clear your 2nd PUC. For pursuing Diploma course, the minimum qualification required is class 10th, but to pursue B.Sc, the minimum requirement is class 12th.

If you clear backlogs of B.Sc degree then you will be eligible to apply for M.Sc in any university including Bangalore University subject to meeting the admission criteria.

If you have 10 backlogs then probably you are not meant for engineering. You might be good at many other things, but certainly not engineering. Why do you want to pursue engineering only? There are many higher education options in Canada which you can pursue. Also, most of the good Universities won't consider you unless you give them a "passed" transcript for all subjects and semesters. I'm talking about good universities. If you really have some good projects and high quality work experience, you can give it a try though.

BCA and B.Sc both are Bachelor's degree. You can do anyone of the two.
Good luck.