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I've read somewhere that the current machine model is not quite fit for functional programming. So what is the limitations of the current machine model? Has a more suitable machine model been developed?

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Landin's SECD machine was one of the first designed to evaluate lambda calculus expressions. Ager et al. cover other abstract and virtual machines designed to do same in their paper "A Functional Correspondence between Evaluators and Abstract Machines".

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Yes, it was developed. Here's an article on Lisp Machine.

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Lisp machines were optimized to run Lisp programs, but weren't machine models. Furthermore, from what I understand, they were still sequential. A suitable machine model for (pure) functional programming shouldn't be sequential.

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