Helium is an inert gas: it belongs to Group VIII. It is inert because the number of electrons is stable. Atoms of helium do not lose or gain electrons, so they cannot combine with other atoms to form molecules. The animation below shows you what an atom of helium is like.
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.
The animation shows electron pairs: since electrons have negative charges, they repel each other so they would normally be at opposite ends of their orbit.