When inquiring if a business is open it is correct to ask if they are open today or "do you open today". Either way conveys the question appropriately to find out the hours of operation for a given day.
It is grammatically correct to say , "I am in school today." This is because you are in the building, not at the building.
yes
Yes, you can say that; we've got today to get this job done.
Yes.
"We were informed it will be corrected today" is a correct sentence. However, it might sound a little better to say "We were informed that it will be corrected today."
It is correct, but it would be nicer to use the baby's name, as in "How is Johnny today?"
Yes, that sentence is grammatically correct.
Yes, "by the end of today" is a correct way to refer to something that will happen or be completed before the current day ends.
Yes, of coarse.
Open-minded is "d'esprit ouvert" is "ouvert d'esprit" (both are correct) in French.
Neither, apparently, see related links.
no you would say we or you me and him!1