I know I ask it for every similar questio n but the usage of articles is still not very clear. So. Why is "Matej is waiting for the food" considered wrong?
The name forms without diacritics have to be added manually for every sentence for every exercise, and sometimes something is overlooked. Here one "Matej" version was missing, and it has been added.
What is the difference in Czech between "Matej is waiting for food" and "Matej waits for food"?
They are very subtle and generally, the only difference is context. If you wanted to say that Matěj waits for food regularly, you could say "Matěj čekává na jídlo." but it's not necessary.
In Czech you can expres the difference (if it is important) by time specification: Matěj právě (or "nyní" or "teď " or "v tuto chvíli" or "zrovna" ..) čeká na jídlo. (Means .. is waiting for..). nebo Matěj obvykle (or "často" or "pravidelně" ..) čeká na jídlo. (Means .. waits for..). Matěj čekává na jídlo can be used for regular or repeated action, it sounds me in this case a bit emotional (imagine something like: poor Matěj .. he usually waits for food..)