The proper phrase would be "Out of the office due to death in the family" Bereavement is an emotion or state of being emotional and cannot be used in this way.
No, the correct statement would be "Is he at the office?" by adding the article "the" before "office."
I am unexpectedly out of the office due to a death in the family. For assistance please contact Jane Doe, <contact information>. Thank you.
Yes that is a correct sentence, as long as you have identified who "he" is in a previous statement.
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principal's office is correct
There are many places where one could receive bereavement counseling. This type of counseling can be found online or in a office. If the person seeking this kind of counseling has access to a computer or phone they could call United Way in order to find a office in their area that specializes in this type of help.
are you at the office
If it is the office of one nurse, this is correct - nurse's office. If it is the office of a group of nurses, this is correct - nurses' office.
I am present in the office today.Today, I am present in the office.
Both could be correct, depending on context
Usually you would say that you were at the office, but saying that you were in the office is grammatically correct as well (as long as you are technically in the office building). "I am in office" without the word "the" is only correct if you are currently holding a position which expires (like President or Chair).
"Out of Office" used to be "Out of Faculty". Microsoft kept using "OOF" when writing about "Out of Office" - so I guess that is the correct term.