The word bot, in Internet sense, is a short form of robot and originates from XX century. The modern use of the word bot has curious affinities with earlier uses, e.g. “parasitical worm or maggot” (1520s), of unknown origin; and Australian-New Zealand slang “worthless, troublesome person” (World War I -era). The method of minting new slang by clipping the heads off respectable words does not seem to be old or widespread in English. Examples: za from pizza, zels from pretzels, rents from parents, are American English student or teen slang and seem to date back no further than late 1960s.
Yes. Messenger bots are approved by Facebook before being made available inside the Messenger app so you can rest assured that they aren’t trying to steal your identity (or anything else). What’s more is a bot is tied to a Facebook page and a Facebook app making it all the more inconvenient to use for fraudulent activity. That said, don’t exchange private and/or personal information with a bot. Finally, because Messenger doesn’t support credit cards and purchasing just yet, anything you buy will likely be done via a browser with a bot aiding you so far as to place an order. If you want, you can always block a bot.