Very true.

밥 먹었어요?

Literally: "did you eat rice?"

Less literal: "did you eat?"

Actual meaning (often, not always): similar to "how are you?" in English.

Koreans that ask you this question don't actually care about the fact you actually ate or not. They just want to know whether your fine or not.

It's like the French asking you "Ca va?". They don't want you to elaborate on your feelings. A simple "Ca va!" is all it takes to have a meaningful interaction :)

"am cooking" is a different tense.

That is present progressive tense