Casaco sounds very similar to cassock. The robe worn by clergy in Roman, Anglican and Orthodox Churches. It's clear the word stems from an older root and evolved over time into its various meanings.
"The word "cassock" comes from Middle French casaque, meaning a long coat. In turn, the old French word may come ultimately from Turkish "quzzak" (nomad, adventurer – the source of the word "Cossack"), an allusion to their typical riding coat, or from Persian کژاغند "kazhāgand" (padded garment) – کژ "kazh" (raw silk) + آغند "āgand" (stuffed). The name was originally specially applied to the dress worn by soldiers and horsemen, and later to the long garment worn in civil life by both men and women. As an ecclesiastical term the word "cassock" came into use somewhat late (as a translation of the old names of subtanea, vestis talaris, toga talaris, or tunica talaris), being mentioned in canon 74 of 1604; and it is in this sense alone that it now survives."
Interesting. There is a Czech word "kazajka", which theoretically can be used as synonymous to jacket but that usage is very archaic. Nowadays it is only used in the phrase "svěrací kazajka", which means straitjacket. But given the root of the word, it probably has the same origin as the Portuguese casaco.
Deixar is the same as Dejar in Spanish. It's one of those weird verbs that changes depending on context. "To leave a thing" is the best way to describe it. You can leave someone to their own devices, leave something in the trash, or even leave an object behind. It's NOT "leave" as in "leaving a place", that's Ir.