Water is often referred to as H two O meaning it has two atoms of oxygen combined with one atom of hydrogen with a chemical formula of H2O (the 2 should be a subscript when normally written).
One of the basic rules of chemistry is that matter is never created or destroyed during a chemical reaction. This is called the law of conservation of mass. This means that in a chemical reaction between elements, or elements and compounds, some chemical bonds are broken and new ones are formed.
In reference to your second question, atoms with electrical charges - called ions - are sometimes neutralized during certain types of chemical reactions but the atoms themselves are not neutralized but are definitely rearranged.
Carbon is unique because it can form multiple bonds with itself and with everyone of the non-metal elements on the periodic table. The result is that there are more compounds containing carbon than all the other compounds formed from all of the other elements combined.