Hello there! 2), 3) and 4) are all correct answers that just mean the same thing. As to the first option, I think that it might be used, although it's not very common! That's it! Hope I've helped you!

Hey Viktoriya (Cool name!), Isn't English weird? Here we have four sentences, all meaning the same thing, and yet... something seems off, right? Well, the truth is, they're all right. So often, and I'm sure you'll agree, language needs to be in context - but the point is, look, you just don't have lollipops! 1 - Normally, this sounds less fluent than one would like and the tone seems to imply a rudeness. 2 - Depending on the context, this could be a bit more formal. 3 - Less formal, and perhaps the way in which you might speak to your mother. 4 - Again, formal, but not quite as jarring as number 1. It's not easy to distinguish formality in English - but 'don't' is always less polite, let's say, that 'neither'. Great question :)

Neither do I. sounds natural

Following up on the previous answer. From my perspective even 1) sounds perfectly fine.