A group of countries under one authority is typically referred to as a federation, union, or confederation, depending on the level of autonomy and governance structure. In some contexts, it may also be called an empire or a bloc, particularly when referring to political or economic alliances. Examples include the United States as a federation and the European Union as a political and economic union.
A group of cells that develops from a single original cell is called a clone.
I'm not challenging your authority. Let's call the proper authority.
It can be called many things. In the USA, we call it the congress (or the senate and house of representatives). In England and other commonwealth countries, they call it the Parliament. In Israel, they call it the Knesset.
The President of India has the authority to call a joint session of the two houses of Parliament in India. This can be done to break a deadlock on a particular bill if it has been passed by one house but rejected by the other, under Article 108 of the Indian Constitution.
Countries?
Yes, in football, the referee has the authority to make the final call.
Sir or Madam (as the case may be).
A person who has the authority to sign a check is typically called a signatory or an authorized signer.
titular
governor
The President
President