Despite being part of the arrowverse, The Legends of Tomorrow seem to operate under different rules of time travel and what can or can not be changed without massively altering the timeline. Still, they appear to operate under some sort of guidelines of when they can, or cannot travel to, or what they can or cannot alter.
The obvious assumed rule, of course, would be that they were not allowed to create paradoxes - deliberately, at least - but their entire original mission was to do exactly that. Killing Vandal Savage at any point in the past as they had intended would have created a paradox, or at the very least, greatly changed the timeline as he was intimately involved with many of the atrocities of history.
The Legends are often directed to eras because of "timequakes" emanating from changes that they must prevent. Because it's a TV show, the Legends always initially fail and have to clean up their own mess - and without fail, people of the time are exposed to unnatural things (e.g zombies, a man made of fire, etc) or things from out of their time (e.g. the ATOM suit, flamethrowers, etc), or change history themselves (e.g. killing a feudal warlord, freeing a plantation worth of slaves). The Legends never seem concerned with the possible consequences of such things, but they acknowledge that tiny things can create huge changes - such as
Professor Stein accidentally causing an altered timeline with a daughter, after he told his younger self to focus more on his family.
The Legends were very unhappy with this revelation.
In a rare explicit declaration in Fellowship of the Spear (S02E15), Rip explains that the events involving Jesus' birth, death, and resurrection are too crucial to even go near, as any alteration could have devastating effects on the timeline, but besides those three points, I know of no other stated rules of when they can or cannot travel to.
Yet, when the Legends discover that an item they seek is in the middle of an active battlefield in the era they are currently in, there is no discussion of "let's jump to a time when this isn't an active battlefield", opting to deal with the active battlefield in a different, far less effective manner. And the show is littered with similar instances where use of their time machine could let them easily fix their problem.
So - given all that...
What are the rules of time travel and what can/cannot be changed?
Has the show explained something that I missed or didn't understand, or have the producers addressed this?