The mental representations we are talking about are you words you say to yourself in your head when you are thinking. They are not something mysterious. However, it is Locke that really brings the idea of mental representations to the fore, an although Kant accepts a Lockean account to a certain extent he really is not taking that as a main theme in my understanding. Rather, he is taking as his them what must exist as a necessary precondition for the possibility of having representations of language in your head and sensory presentations. Not representations are always lossy, i.e. abstractions of actual sensory presentations. It is the necessary conditions of the possibility of experience that are the transcendentals of Kant, not some dogmatic invisibles that cannot be verified. Also his ideas do not have a lot to do with Plato, but rather are a direct result of his reaction to Hume, but also Leibniz and of course Spinoza and Descartes. He is basically trying to build a foundation underneath the physics of Newton, and so the structure of his philosophy is influenced a lot by the structure of the Calculus that makes the description of nature though laws possible. The key idea is the difference between Analytic and Synthetic judgments and the difference between A Priori and A Posteriori judgments The whole thing is about the nature of judgement. And judgments are something that can appear as statements in language once they are formed. Basically he is attempting to prove that there is something called the A Priori Synthetic and that is the Singular Space and is the basis of geometry. Today we would say it is spacetime, and would not separate out the schemas from spatial representations such as you get in geometrical proofs. Sensation is appears in a manifold which is an A Priori synthesis. On the basis of that perception then there is the apperception of concepts that are then represented in the proofs as statements and diagrams of the geometrical situation, or equations for instance related to the calculus.
But the key point is that we project the a priori synthetic singular that then is the basis of the unity and totality of the manifold which then appears as a perception of something that gives rise to an apperception. When we consider that thing as a physical object we project on it the Categories which all objects share such as quality, quantity, relation and modality. The key to this projection is the positing of causality. Because causality comes from us, then we do not have to find it somehow in the world as an objective thing, and that is why Kant believes that the only road to Transcendental Reality is via Transcendental Idealism. A good source for further understanding is the Bernsteintaps.com lectures which goes though all the arguments in detail. Our tradition has been basically critical and idealist after Kant because his arguments for his position are so strong. He would have considered neural activity part of the noumena. Until we can relate the neural activities in fMRIs to what is actually experienced in consciousness I think it would remain part of the noumena even though we can now see it by peaking inside the functioning brain. It still does not relate to our experience, and in fact the more we find out about it the more mysterious it becomes because of its decentralized processing.
Suggest you read the Patton Commentary on Critique of Pure Reason if you are interested in finding out more information about Kant’s philosophy. There are a lot of strange interpretations of it out there and strangely it is hard to find a good commentary even though it is one of the most commented on books in our tradition. It is so complex that it is possible to make almost anything you want out of it. I went though a lot of bad commentaries before I found Patton. Basically he turns each sentence into a paragraph and keeps the context within the overall argument in mind as he unpacks each new sentence.