“This is a really good Sunday.” would be a better choice. however, we (americans) wouldn’t say that, it just sounds odd. are you saying that it’s good because the weather is good? then you would say: “it’s really nice out today.” are you trying to say that you’ve had a good day because it was fun and relaxing? then you would say: “it’s been a GOOD day today” (emphasizing GOOD). are you saying that, in general, Sundays are good for you? “Sundays are a good day.” or “ I LOVE SUNDAYS! they’re always a really good day.” we usually don’t reference the name of the day in everyday, casual conversation unless you’re emphasizing it for some reason. if you give some more context we can help with a better answer. hope that helps! 😉

#2 is grammatically correct and is most often used. #1 is from an American dialect and implies a less educated speaker.

Both are correct. In British English you’re more likely to hear “really”. I believe both are used in American English, but “real” is more informal.

This is a really good Sunday is correct.