"The meal is on us!"
Does עלינו mean the same as the English “on us” in this context? Namely, “we are paying for the meal”?
I wrote ארוחת as I would for breakfast / lunch / dinner. Here it says ארוחה so what is the general rule?
The word "ארוחה" means meal. In the construct state, its 'ה becomes a 'ת, which is common for words that end with 'ה.
אלינו is to us. (אל means to)
עלינו is on us (על means on)
There is a typo in your נמצה. You mean נמצא which is still wrong. You use נמצא when talking about a location.