Using only basic gates

Hi,
can I use components that I already built (by basic gates) in exercises that say using only basic gates?

also, in exercise 7, it says basic logic gates, does that include basic arithmethics?

If the question says only basic logic gates, then you must use only basic logic gates, nothing more.
If you would like to create sub-circuits using basic logic gates and use multiple instances of these sub-circuits, that is fine.

Basic logic include NOT, AND, OR, NAND, NOR, XOR, and NXOR only. Please see the footnote in instruction #14 b.