Hydrogen has an atomic number of 1. This means that hydrogen atoms have a single proton. They also have a single electron: this is lost when a hydrogen atom turns into a hydrogen ion.
Electrons have a very tiny mass: they don’t have “Zero Mass” as it says in the animation. However, you don’t need to take account of their mass when you are calculating molecular weights: for your purposes, the atomic mass is calculated by adding the number of neutrons to the number of protons.
Since electrons do actually have some mass, they cannot travel at the speed of light. They would need an infinite amount of energy to travel this fast. However, they do buzz around the atomic nucleus at very fast speeds.
When an atom is excited, ie. it has too much energy, electrons can escape from their normal orbits into higher energy orbits or escape the atom completely; this would leave the atom in an ionised state.