It's a subtle difference, but that would be "Jeg bruger din sko". The plural is indicated in the din/dine rather than the noun itself here.
Is it also correct to translate it to: "I am borrowing your shoes"? does "bruger" also translate into borrow?
Not really, I would use "at låne" to mean "to borrow". Jeg låner dine sko = I am borrowing your shoes
Does bruger give me the meaning of "I'm wearing your shoes"? Or is it like "I'm using them to kill a cockroach"?
Like in english it could mean that you are wearing them (or using them for something else) but if you want to be precise you could say "jeg har dine sko på"- i have your shoes on.
Portuguese uses usar to mean wear, but I've never heard a natural English speaker use to use with respect to clothing or shoes.