No. We still have a poor understanding of the exact way neurons code information and store information.

This page shows some of the current theories: https://en.wikipedia.org/wiki/Neural_coding#Hypothesized_cod...

The problem isn't whether there is "a" way; the problem is there's a multiplicity of ways and we don't know what the best one is. Part of the reason we don't have any idea what the best is is that we can't even construct any of them from a real brain, that is, the "brain scanning" technology the techno-rapture-style Singularity expects to develop does not even remotely exist right now. So we have nothing to experiment with or gain any experience with. The only ones we'd even remotely have access to right now would be some rather brute-force encoding of neurons and connectivity strengths and we pretty much know that such a thing must be incredibly redundant, but we have no ability right now to remove that redundancy. And we can't do it on a very large neural set.

It has been done on small models, though, at least to some significant extent: https://en.wikipedia.org/wiki/OpenWorm

most definitely. ANN's do just that.

That said, they assume a computer. and a program to run it. Similarly, the brain probably has many complex lower structures that compress language storage, but the compression software is not trivial to store itself.