Help me with the usage of "the" and commas

Our work involved [the] complete design of a transformer.

Do you have books?
Do you have [the] books?

Both make sense to me. The second sentence suggests that the reader knows something about the books.

I was involved in [the] testing and verification of the satellite.

Can we use “the” before scientific principles?

I want to learn about [the] gravitation.

My main goal is to learn and [to] earn first rank in the exam.

Can we combine singular and plural objects?
" I need an apple and many bananas"

Comma before “using” needed?

I designed the car when I was working, using several tools.