1) 저하고 같이 커피를 마실까요? 2) 저하고 커피를 같이 마실까요? Which one is more natural & grammatically right? - Both are all correct and natural. Korean sentences have flexible word order. So those two sentences are grammatically correct. And when saying in a conversation, some constituents or case paeticles can be left out in a sentence. (저하고) 같이 커피(-를) 마실까요? (저하고) 커피(-를) 같이 마실래요? (우리가 함께/같이) 커피(-를) 마실래요?/마실까요?

I usually use this line: 저랑 커피 한잔 마실까요?

이랑/랑, 와/과, and 하고 are all ways to connect nouns ("and").