There are a couple of things that are worth knowing.
First the rice needs to be right kind - I recommend Basmati (or less preferably, Yankee long grain), because the cooked rice will then remain firm and dry when cooked. At the other end of the spectrum, if you use Thai or Japanese rice the result will likely be a gooey mess. Horses for courses, so to speak.
No need to make the omelette, nor would most restaurants or takeaways - who has the time to fry the eggs and chop the omelette into tiny pieces? In fact you do not even need to put the eggs in a bowl and beat them.
All you need to do, is to put the cooked rice into a hot wok that has been sufficiently coated with oil (Chinese swear by peanut oil - but the difference is small), then use the ladle to shape the rice like a volcano (big dimple in the middle), then break all the eggs into the dimple fairly quickly, then stir the egg up a little within the dimple before stirring it all up together with the rice - that's it! If you stir them all together quickly (before the egg has a chance of being cooked when it hits the metal surface of the wok), the eggs will be in teeny tiny pieces, if not, you will get some larger "omelette like pieces" - your choice, and control is easy once you get the hang of it, if it matters to you!
For added flavour, I recommend some Maggi liquid seasoning or variants (cheap in big ~700ml bottles in Chinese supermarkets, small 100ml bottles are at nearly the same price:damn:in normal supermarkets) if you think salt boring - the stuff is far more tasty than conventional soy sauce. You can add chopped spring onions, char siu, prawns, petit pois, sweet corns etc. if required.
BTW anybody who eats rice regularly is mad not to buy a rice cooker. Don't bother with them imported ones sold in Chinese supermarkets - some are ridiculously overpriced. Tefal's 8-in-1 is a fab machine for a reasonable price:
https://www.amazon.co.uk/Tefal-RK30...r_1_1?s=kitchen&ie=UTF8&qid=1483209137&sr=1-1.
Cheers!