Learn English – Why do you say “so do I”

"Do I love you?" is the proper form. In spoken English, though, you can, and in suitable situations you would, use the form "I love you?"

To put this into an example (spoken):

Situation A:

Person A: "This guy came in and asked whether he can borrow my cell phone. Do I know him?"
Person B: "Yes, he's one of our former employees, we've worked together long time ago."

Situation B:

Person A: "Have you heard? Some guy went to the bank today and started shooting people.
Person B: "Yes, it is kind of sad, because he's one of our former employees. You two have worked together long time ago."
Person A: "I know him??"

In situation A, you are really asking the question, because you want to know the answer. In situation B, you kind of already know the answer, but for the matter of the situation, you want to assure yourself, as if to not wanting to believe the result.

In writing, you would almost always use the (proper) first form of your questions. The second form is typically only used in informal speech, and generally accompanied by a generous dose of disbelief (sometimes even outright sarcasm), with heavy emphasis on the why/how.

I would see it as a way of intentionally beginning the sentence as if you were making a statement, and then, as though suddenly stumbling over an internal doubt, turning it into a question, encouraging others to recognise and share that same doubt.