No, water polo originated as a form of rugby football played in rivers and lakes in England and Scotland and since rugby originated from football (or soccer) then this is the oldest surviving team sport. Waterpolo was the among the first team sports introduced at the modern Olympic games in 1900
Ayurvedic medicine is the oldest surviving healing system
The oldest surviving staircase in the world is Stairways in Persepolis. They were built in 550 B.C.
Discovery
Probably the Bible....
Obviously, the indigenous Australians, or Aboriginal culture, is the oldest surviving culture in Australia. They were here long before the Europeans.
Clement of Alexandria
Tanfield
yes
Windsor Castle
A.J. Foyt is the oldest surviving Indianapolis 500 winner.
It was compiled quite a bit before the 4th century, but that is the oldest surviving copy. The "Tanakh", which is the Hebrew Bible is the original version and our modern Bible is based on that.