1) It's unclear which parts of our perception reflects the real world and which don't, and also how to measure how accurate they are. We obviously see objects as much more than what the photons representing them that hit our retina tells us. The brain creates all kinds of backstory and assumptions based on its model of the world, however, I would argue that the basic shapes we see are accurate.
So basically the geometry/shape of a face, of a chair, of <pick any object> is real, while the extended cultural, practical and personal associations the brain attaches to those are "not real" (or rather, we see a chair as a utility we can sit on, so we see both the shape of a chair but also potential uses for it, so it becomes an extended model of ourselves+chair, but that doesn't mean the shape isn't real). Also even though we can change our extended model of objects, we don't normally change our base perception, e.g. a chair always looks the same shape even though we may see different uses for it in different contexts. I would argue we really see the shape of the chair. This then leads to difficulty knowing how to define what is real/accurate and what isn't.
2) It's unclear whether the extended models we have are reflective of the real world or not, and if so how much. Just because I see a chair as a utility I can sit on, doesn't mean that it doesn't reflect reality. In fact you could say the model reflects a more abstract truth about how my body fits into a chair, so it becomes a more encompassing truth about bodies+chairs. Hell you could even include that it includes some information about how my muscles tire and need rest and so on.
3) I think the basic idea is true and interesting. We clearly do not see the world like a camera does, but I wouldn't go as far as saying it doesn't reflect reality at all. I haven't looked at this authors papers, but I saw an interview where he mentioned some statistical measurement of how organisms who saw the world as it actually was had a lower survival rate than those who do, and I'd be curious on how sound that argument is. The devil is in the details again and it sounds to me like such an argument could be interpreted several ways.