Yes, the Chinese people do eat omellete with rice for lunch / dinner. The red bell pepper is used for colour mainly. I always add a half egg-shell of water when I beat the eggs, that’s what my dad has always taught me. Perhaps it makes the eggs lighter and fluffier.
Season the egg mixture with salt and pepper. Sautee the diced green beans and red bell pepper in a wok with sufficient oil until the green beans appear to be a of shinier, richer colour and then add in the beaten eggs. Make sure that there is enough oil on the wok before adding the eggs (even if you use non-stick wok).