No of course not. You don't need a passport to travel within one federal country!
No, you do not need a passport to travel to Florida if you are a U.S. citizen.
Yes, your child will need a passport to travel to Mexico by air.
Yes, a child needs a passport to travel to Mexico.
No!
Yes if you are to travel by air but if it is by sea of land, no need but you need a proof of identification and the passport is the best one you have for the child.
No, a passport is not required for domestic travel within the United States.
If you are a US citizen, you will need both a valid US passport and an Australian ETA visa to travel to Australia.
no
When traveling from Puerto Rico to Florida, no passport is needed. Puerto Rico is part of the US, as is Florida. Traveling from Puerto Rico to Florida is travel within the United States. Citizens do not need a passport to travel within the US, although they do need some form of government-issued photo identification to get on a commercial airplane and a passport will serve that function. Non-citizens who are in Puerto Rico have already entered the US using a passport (or similar document for Canadians) and so need only the identification they would need to travel within the US, for example, from Miami to Atlanta, to travel to Florida or other locations in the US.
Key West is a city in Florida. Provided you are a U.S. citizen, you do not need a passport.
No but they need a passport if they live in Canada.
If you are going on a cruise from a US port and the child is a US citizen, you will only need a state-issued copy of the child's birth certificate. If you are flying, the child will need a passport.