Is my answer correct? "Does 7 p.m. this Saturday works for you?"
Yes. 7 p.m. is fine. I will meet you this Saturday at 7 p.m.
It's correct, but informal. And when "do" appears as an auxiliary verb, the main verb (in this case "to work") is never conjugated – therefore your sentence should say: "Does 7 p.m. this Saturday work for you?"
[Not a teacher]