There are many types of weapons and if you want to give an individual skill to each of them it will lead to some inconsistencies.
For example tell me an action that can be done with a longsword but not with a shortsword or a scimitar.
"Prise de fer" maneouvers. Scimitars do not have point and shortswords are too light and short, usually.
but yeah, it's a good thing that your weapon choice means something. It´s not the same wield a longsword or an axe.
I did not find the cleave feat in 5E (but great weapon master lets you attack again if you crit) but it was a feat in 3E. The spear ability looks similar to the charger feat.
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Not exactly, "Charger" lets you attack after you dash: I.E: you charge and lunge at the end. Rush as described lets you hit nearby enemies in the trajectory of your run.
I do not think that´s even a thing in 5e. Looks pretty cool.
