Shadow kill, does it remove loot from bodies

No. As far as chaos is concerned, kills are kills, so long as it happens by your hand.

(Now luring guards and weepers into conflicts with each other, that's fair game.)

Unconscious bodies are vulnerable to being eaten by rats. You can store them in garbage bins to make them completely safe. The same holds true of corpses. There is also an ability that turns corpses you kill (level 1: stealth kills only, level 2, both) to ash, making it a non issue.

A kill is a kill where Chaos levels are concerned. Tucking the bodies away/disposing of them helps prevent you being detected in mission, but if they are actual corpses they're going to contribute to potential chaos level increase regardless.