This sentence is ok. It's kind of redundant though. Just "How was your day" sounds better.
As 'today' is the current time when the sentence is used, it does not make sense to say 'by today', as today has already been reached.A better way to phrase the sentence is 'Do you need it today.' This sentence makes sense, as it is possible for the action to be carried out at a later time on that day.
Today is a noun in that sentence.
The subject in this sentence is "today," and the verb is "is".
Yes, certainly. 'Today is the first day of the rest of your life.'
Yes. Today is the subject; has been is the verb.
Today is the coldest day of the year.
It's not wrong, it's just not on the right day. Send valentines on the right day. Remember, it only comes once a year.
i had a better day today.
It is a gloomy day today!
It has been a supercalifragilisticexpialidocious day for me today.
These are both acceptable although people would be more likely to ask "what day is it?" than "what day is today?".
You can use "today" as a noun in a sentence like this: "Today is the perfect day to start a new project." In this example, "today" refers to the current day as a specific time period. Another example could be, "I have a lot of tasks to complete today." Here, it emphasizes the day as a unit of time for activities.