[teraflop]

Well, to be clear, particles and pronouns are very different things. (In fact, Japanese pronouns basically just act like nouns, from a grammatical perspective.)

Japanese is a so-called "pro-drop" language, which means it's normal to omit pronouns completely when they can be inferred. "Watashi wa tabemasu" would only be used for specific emphasis, as in: "I specifically (as opposed to somebody else you were just talking about) am eating." In any other context, it sounds unnatural, and you would just say "tabemasu" even in formal situations.

Separately, you can omit particles in colloquial speech when they're obvious. So for instance, in a polite setting you might ask "ashita wa, nani wo shimasu ka?" (meaning "what are you doing tomorrow?") But in a casual environment, you could say "ashita, nani suru?" and still be understood perfectly.