Are there further discussions, examples or proofs regarding killing the five animals on Shabbat, particularly for killing scorpion in Chadayev?
timna, port;and, OR
The five species to which you refer are merely examples of species that are automatically dangerous (scorpoins that are not from Chadayev it appears, do not belong to this category). Consequently, the Shulchan Aruch (without actually mentioning these five species) rules that one is permitted to kill any species of wild animal or of vermin that are known to be dangerous, even if they are not actually chasing him. And the same applies to other harmful species that are not necessarily life-threatening (such as snakes and scorpions in a place where they do not always kill), if one is actually being chased by them.
Otherwise, he is permitted to trample on them in a way that it looks as if he happens to be walking in that direction or even to trap them by placing an overturned vessel on them (Mishnah Berurah).