The point is, is "eat lunch" wrong??

To "have lunch" and to "eat lunch" is synonymous in English

"I eat lunch between the bank and the hotel"

You used the wrong word.I HAVE lunch between the bank and the hotel.

Hmm :/

I'm = i am !

Why is it "i am having lunch" and not "i have lunch"? Is there something i didn't see, that shows, that present progressive is needed?