Thank you very much to everyone who responded1 I appreciate your help.

You need to add "از" after روز which represents exactly the equivalent of "day of" in your second sentences, so they'll be like: امروز چه روز از هفته است؟ و دیروز چه روز از هفته بود؟. These sentences are correct and everyone will definitely understand you, but they're not common at all. Your first sentences, امروز چند شنبه است؟ و دیروز چند شنبه بود؟ are totally correct and common.

امروز چند شنبه است؟ دیروز چند شنبه بود؟ فردا چند شنبه است؟ First versions are correct.. :)

سلام بهتر هست بگید: what day is tody به اون تعبیر که استفاده کردید نیست