1. when a man goes back in time and kill myself 5 minutes before past-him makes the journey 5 minutes into the past to kill himself, he stands over the dead body of past-him and nothing special happens, meanwhile, in the timeline he came from, he had simply entered the time portal and disappeared.
This is because there exists parallel timelines, NOT branching timelines, PARALLEL timelines, meaning that instead of a single timeline that gets divided up by all future possibilities at any given moment, an entire separate timeline exists for every possible combination of possible states that the universe can take between it's big bang and it's big crunch, and this accounts for all the possible states the universe can take as a result of time travel.
Time travel involves the movement of whatever is traveling from it's location in timeline A, to a previous point in timeline B, but since the states that the universe took up in timeline B were identical to timeline A up until their arrival, it might as well be the same universe.
Nothing happens to the self-icidal traveller in the opening example given because he was not strictly assassinating himself in the past of his timeline, but rather, he was assassinating someone who was identical to himself 5 minutes ago in a universe that is identical to the one in his home universe five minutes ago, he may never realize this, and he can never go back to the timeline he arrived from, if he goes into the future, he instead arrives at a future point in the timeline he had departed from.
2. The butterfly effect is merely meant to demonstrate how the cumulative effects of a small event can create a larger event over long periods of time via extended chains of cause-and-effect, and how this process makes it difficult to make predictions about the future, it says nothing about whether actions committed in the past would produce positive or negative results, nor whether they WOULD even produce a large-scale result, it only states what COULD possibly occur over time, they COULD also create positive large-scale effects, negative small-scale effects, positive small-scale effects, etc. the multiverse is not a sentient being, it cannot tell, nor can it care, what a bipedal ape on a speck of dust thinks positively or negatively of, the butterfly effect applies to the effects of the present on the future exactly as much as it applies to the effects of the past on the present, in fact, the butterfly effect was only intended to explain how cause-and-effect chains operate from the present, it was never intended to be applied to time travel, also time travel to the past is actually more likely to produce a positively received result due to you having more information to make a decision in the past than if you made it in the present, there is no such thing as "fate", only hard determinism.
3. the multiverse has three parts, a core, which produces a set of natural laws that all timelines abide by, timelines, that are arranged around the core in ellipses, and which all intersect at the two universes at the state in between the big bang and the big crunch, located at the furthest points on the ellipsis from the core, making all the timelines form the shape of an ovoid around the core in the center. there are also other multiverses, one for every unique set of natural laws, most of which are lifeless, collectively, all multiverses, along with the "space" they inhabit, are referred to as "The Omniverse".