"I stopped smoking three years ago."
Would [ 三年前にタバコを吸うのが辞めました ] be an acceptable way of saying this? Since [ 吸う ] is 'to smoke', and the sentence implies the smoking of tobacco/cigarettes, isn't it more accurate to use both [ タバコ ] and [ 吸う ] to show this? My translation of [ 三年前にタバコをやめました ] is more like 'I stopped (doing) cigarettes three years ago'...
For 前 and 前に, general casw is that if the action occurs throughout the time period, don't use に. If the action happened at a point in the time period, use に. やめる is an instant action so we use に. For more info http://maggiesensei.com/2016/01/28/time-expressions-with-and-without-a-particle/
You can ask a dictionary to help you in cases like this (for example jisho.org, it's really good).
やめる in this sentence is 辞める, it means to resign, to retire, to quit, to leave (one's job, etc.)
やる (or conjugated やります) means to do, but it's more colloquial than する; it's written in kana
やめて is the te-form of the verb やめる. It basically means to stop doing sth. It's written in kana
All three verbs are transitive. I don't really know what you mean with やす and in which context you encountered it. But I hope I could help you with the other three words ^^
Can 止める (やめる) also mean quit doing something? Quit in that context wouldn't necessarily imply a job and it's common to say "quit smoking" in English.