"건축가가 평일에 근무해요."
Translation:The architect works on the weekdays.
Any time there is a choice between native and 漢字-based terms, the 漢字 is usually more formal/official. In many cases though, the 漢字 has fallen out of use and simply sounds weird, so only the native term is used. But there are also many cases where the native terms sound archaic and have been replaced by 漢字-based terms.
In this case, 일 is the native Korean root. When in doubt see if wiktionary has the info. -하다 just makes a lot of nouns into verbs, afaik it doesn't reliably (if at all?) help with figuring out if that noun is Sino-Korean or native. It's the make/do in verbal phrased nouns like "to make dinner/tea" "to do homework/the math/something crazy."