why does it need 와 and 함께? the 함께 made me think it would be something like "let's ..."
The Korean should have 저는 or 나는 or some form of 'I.' Otherwise, I can see it being a little confusing
The subject is often omitted in a sentence when a person is talking after the first use, until the subject changes to someone/something else.
It's only confusing if you're trying to interpret it through English grammar, you'll have to get used to it since dropping the subject is commonplace in Korean (and many other languages)
I'm not Korean but my 1st language usually drops the subject most of the time too. It's obvious here that it's an "I" statement, even without context, because the speaker would specify otherwise.
Why not "I eat a banana and coffee together"? Hamgae is "together", isn't it?