Mantle Scarves

A bit like a short coat that extends to about the size of length, often made of dyed materials, either with or without sleeves, which can be buttoned or wrapped around their bodies, often with either a hood or scarf attached. As far as I know they exist and are usually designed for women. I often speak of a coat, but I am looking for one in real life and I was wondering if there is a particular word to describe them today.

I think you mean a cape (that's what we call in the UK anyway)

His name, shrugging his shoulders;)

Shrug of the shoulders: a small length (sometimes less) jacket.

A poncho?