The fruit is called carambola -- although it is actually also referred to as "star fruit." For more information on the carambola -- plus photos -- see the Related Link.
Fruit Ninja
Plantain
Physalis and Plantain
coconut
Yes, but it is small. Its name is Surinam Cherry. Follow the related link for an image.
Kumquat
New Zealand looks after the slice of Antarctica called the Ross Dependency.
Japanes flag
The mathematical name is a sector.
The name of a four sided shape that looks like a kite is a diamond.
A name of a fruit is a common noun. If you actually gave your fruit a name, like Arnie the Apple (note the capital letters), then that would be a proper name.
Pillow lava got it's name by the it looks. It looks like pillows.