You are correct, on both counts.
However, you must understand Islam properly, the meaning of “ilaah” and “ibaadah.” The second word loosely means worship, but it is talking about any act of submission or servitude, and prayer in Islam is considered “ibaadah.” The first word is loosely translated at “god” but literally it means anything–absolutely anything, which is worshiped.
So if, in Islam, a person prays to someone or something, they are worshiping that someone, and if they are worshiping, it makes who or what they worship an “ilaah” or a god. Which is how, in Islamic theology, the prayer and revery of Mary by Catholics is considered worship, making her an ilaah or god.
The Qur’an also says that Christians worship their priests. You might balk at that as well, but because they are allowed to make things lawful and prohibited, according to Islam they are worshiped.
So the issue isn’t what Christians think they’re doing, but rather how what they do is described by Islamic terms, which is why the Qur’an is not incorrect at all.