First, Systemic Functional Grammar. My theory is related to this one and it has influenced my thinking. The notation system used for relational networks is an adaptation of the network notation developed by Halliday. My theory is also a functional theory of language. The main difference is that Systemic Functional Grammar looks at language primarily in its relation to society and social interaction, whereas neurocognitve linguistics looks at language primarily in its relation to the brain.
Generative grammar is quite different.
It is not a functional theory, and it is very heavily influenced by the methods of Bloomfield and the neo-Bloomfieldians. This fact is ironic since Chomsky criticized behavioral psychology and said that he was interested in the mind. So although Chomsky was correct in thinking that it is important to consider the mind, he never quite succeeded in actually considering it. Nowhere in his writings do we find any real discoveries about the mind, and nowhere do we find him trying to incorporate any findings of neuroscience into his theories of language. In short, generative grammar neglects both of the requirements for a neurocognitive theory of language that I mentioned in my answer to your third question.