How does Nirvana fit into theory of evolution? Can nirvana be called as some sort of directed evolution? Can a Buddha or Arahat be considered as an evolved being as compared to the rest?
The scientific definition of evolution is as follows:

Evolution is change in the heritable characteristics of biological populations over successive generations.

There is no guarantee that the offspring of a Buddha or Arahat will be an enlightened being, i.e. these characteristics are not guaranteed to be passed on to their successive generations (Not a very rigorous scientific answer but I hope you got the gist of it).
Another way to think about it is that

Has it been experimentally proved that Nirvana fits into the theory of evolution? OR, Can we design an experiment that can show if Nirvana fits into the theory of evolution?

As far as I know, these questions can not be answered as of now (Perhaps no one has tried to do it). So from a scientific point of view, I would say 'no'.