Apure substance containing only one kind of an element is always uniform all the way through (homogeneous). an element be separated into simpler materials (except during nuclear reactions). over 100 existing elements are listed and classified on the

1. A pure substance containing only one kind of atom.

When a substance has more than one kind of atoms, it would be called a compound. A pure substance can be made out of an element or compound as long as there is only one kind of them, but this question seems to ask about elements. 

2. An element is always uniform all the way through (homogeneous).
An element cannot be separated into simpler materials (except during nuclear reactions).

An element is the simplest form of material that can't be separated. The example would be oxygen(O2) or hydrogen(H2). An element doesn't mean it contains 1 atom because many of the stable structure made of 2 or more atoms. Normally, you cant separate O2 into two oxygen atoms.

3. Over 100 existing elements are listed and classified on the periodic table.
The periodic table used to classify element and make it easier to understand. The classification based on the atomic number and the electron configuration of the elements.
The element in the same column could have similar traits so that they can be put into a group.