What is the proper answer to: "What I am about to tell you is the truth. What I just told you is a lie. Do you believe me?"?

It's a meaningless rhetorical construction. No statement is actually being made. The first sentence refers to a promised future statement. But when that statement comes, instead of actually stating something, it simply points to the previous sentence, which itself wasn't a statement--it simply pointed to a future statement. So each sentence points to something that doesn't actually exist. It's like saying, "I'm going to say something. I just said something." It just goes around in circles without ever arriving at a statement. There's no actual "something".

You can't believe. It's like "I'm a very bad liar", but maybe that's a lie?

The overspray from my windshield washer fluid just totaled a smart car.

so what?