This is quite a strange sentence... if you want to say this in a restaurant context, you would say: האוכל מגיע. Maybe I am missing the intended context here, but if not, the sentence should probably be changed/removed.
Assuming you are a native Hebrew speaker (like me), I can see why you'd say that, but it's debatable. If you you want to speak "proper Hebrew", or want to write it in a newspaper or a book, then בא vs. מגיע should be pretty much like "come" vs. "arrive" in English, and here it should be בא. I believe that several decades ago all Hebrew speakers would speak this way, too.
In recent years מגיע has been gaining ground over בא by Hebrew speakers (for "come"; בא has been gaining its own ground over other words in different meanings...). So now indeed you're more likely hear האוכל מגיע. But I hope it's not yet a sweeping victory. FWIW I would still say האוכל בא - at least I hope I would, I could be misleading myself...
There is no technical problem with saying "אוכל בא". The problem is contextual and it might not be understood, and sounds extremely awkward on its own. Here is why: Hebrew has no 'progressive' tense (like most languages), and it is derived from the context.
So if you translate to English, "האוכל בא" would like "the food is coming" (although also awkward, as I pointed out in my previous comment), while "אוכל בא" would be more like "food comes". You can see that even in English, saying this separately without any context would be extremely strange.
I don't have the Hebrew alphabet to answer the question correctly.
Does anyone here an 'e' before the 'ba'? "HaOkhel E'Ba" is what it sounds like
Hebrew has a soft sound after L, similar to French but different from English. This might be why you hear this.
The use of the definite article here is good Hebrew, but poor English where a better translation would be the indefinite expression 'food is coming".
The meaning of "The food is coming" differs from "Food is coming" both in English and Hebrew.
This course is ridiculous! Why is it testing on words it hasn't covered yet?