Valence electrons are the electrons in the outermost shell of an element on the periodic table. Atoms want to be able to have a full outer shell and they can share or trade electrons in order to achieve this. Valence electrons are also super super important in chemical reactions. The number of valence electrons determines what group that specific atom or element is in on the periodic table. This affects the reactivity of the element.
It is the concept of surface tension that helps the coin to float on the top of the water in the glass. The surface tension acts just opposite to the gravitational force and that is why when any metal placed in the water it will float and come on the surface. Hope this helps!