Can a person have multiple Citizenship?

No, India and Japan do not allow dual citizenship!

The other countries do. France and Ireland apply to jus sanguinis (Latin: right of blood), a principle of nationality law by which citizenship is not determined by place of birth but by having one or both parents who are citizens of the nation. The United States apply to birthright citizenship (jus solis).

A person born in the United States to a French and an Irish parent acquires three citizenships at birth and has the right to get an American, a French, and an Irish passport.

Should this person immigrate to New Zealand s/he could get a forth passport of New Zealand after having met the naturalisation requirements..

Provided all of the countries involved allow dual citizenship then yes

The Republic of Ireland, France & the US allow dual citizenship but Japan & India do not so you could hold Irish, French & American citizenship simultaneously

There are people who have 5 citizenships, but they are rare. The key is that every country involved plays along. In your example, India and Japan do not allow its citizens to hold another citizenship, so that wouldn't work.

Any country that allow dual citizenship, you can be a citizen of that country if you fulfill the timeline requiremnet. Say if you want to be a citizen of 10 countries, it's up to you. But some countries won't allow you to do that and they will force you to renounce the others and just keep their nationality.

Yes. Aust and NZ here