In the first and fourth statements, you put "the" before "new day", but this is incorrect as there is not only one day. The way to correct this would simply be by using "a" instead. In the second case you put "the" before "morning". This statement is very weird in that it sounds more than just unnatural to the point of being grammatically incorrect, yet I can't think of why it would be. In cases like these, we don't put "the" in there and just say "Be morning." In the third case you're talking to the sun as if it were a person, so just as you would not say "the steve" you cannot say "the Sun". Other than those small syntax errors, your sentences were perfect. I personally might say, "Why can't it be morning, already?" Note that in formal writing you would have to have a comma before "already", and it would be more fitting to put a comma after "Come on," and if you're intending exasperation and impatience an exclamation point at the end. Hope this helps! I originally wrote this as a comment, but it ended up kind of long so I moved it to an answer.

Edit: I rewrote my comment as an actual answer because it got a bit long.

"Come on already" and "hurry up already" are good expressions to know for when you're impatient with something. I personally would never urge on the new day; I'd go to sleep. If I were excited for it, I'd say something like, "I can't wait for tomorrow."

They are all fine. These statements are very personal, so a lot of variation is possible.The only one I question is the 3rd with 'the Sun'. It doesn't quite sound right to me. I'd change 'the Sun' to 'Sun'. For some alternatives, here's how I'd write them. My versions are less poetic than yours. - Come on. Be the new day already. "Come on, let it be a new day !" - Come on. Be the morning already. "Come on, let it be the morning !" - Come on. Hurry up and rise, the Sun. "Come on, hurry up and rise, Sun." - Be the new day already. "Let it be the new day already".

“When will it be morning?” — that’s good. “Be A new day already.” “Hurry up and rise, Sun” (note: not “the Sun”).