According to some Bazi schools of thought, the 7 Killing Star is the most important 'power' star that one must look for in order to achieve success. Yes, all 8 characters must be considered in a chart. But once the 7K star exists in a chart, all other stars must be evaluated with this 7K star as the singular point of reference. If the Day Master is weak, elements that suppress / mitigate the 7K star are Useful Gods. If the Day Master is strong, elements that support the 7K star are Useful Gods.
In fact, some Bazi schools of thought do not consider the seasonal strength of a Day Master at all. What is most important is whether the chart gets the job done, and whether the work done is efficient & effective. 7K uses the shortest time to achieve the greatest result, but may resort to unconventional / unscrupulous means to get it, ignoring proper protocol. Some people might get hurt. Its level of aggression is arguably the highest, with Hurting Officer at a close second.
七杀 is associated with death, but it also represents swift aggressive execution of plans. If you need to use it, do so with care. Proceed with caution.
In 奇门遁甲 (QMDJ), as mentioned, we have 天柱 (Heavenly Pillar), also known as 破军. We have 天蓬 (Heavenly Grass), also known as 贪狼. But there is no 7K star. However, the 'Star level' is only one of the 5 levels that QMDJ operates at. There are: Palaces, Stems, Deities, Doors & Stars. The first 3 relate to Earth. The Doors relate to Man. The Stars relate to Heaven. (This is my own simplified version. No offence to other QMDJ schools of thought.) Also as mentioned, 死门 (Death Door) is associated with 坤 (Kun) which is synonymous to the lunar 7th month as well as the 7K star. Doors represent the most practical way to win a battle, but the fast results come and go easily. The Death Door is the last door we consider because it is the most inauspicious & least practical of all doors. We do not conventionally use this door except for anything associated with death: funeral processions, worship of ancestors & spiritual pursuits.
In 紫微斗数 (ZWDS), 7K is one of the stars that form the 杀破狼 (Sha-Po-Lang) formation. This formation is, like Bazi's 7K, the most aggressive of all formations in ZWDS. 杀破狼 (Sha-Po-Lang) is made up of 3 stars that are previously mentioned: 七杀 Qi Sha (7K), 破军 Po Jun (Broken Soldier) & 贪狼 Tan Lang (Greedy Wolf). Here, the meaning of 7K reverts back to the Bazi system of fast & effective results. But do use Sha-Po-Lang with discretion. Minimise aggression.
There are quite a few youtube videos that have both positive & negative remarks about Sha-Po-Lang. It is traditionally seen as an inauspicious formation. But in these modern times where change is the only constant, we may have to see this formation a bit differently. This is a video that has a more positive view of SPL:
That being said, the criteria for success does not only depend on the presence of SPL in one's ZWDS chart. Other compatible stars must be present in the 4 main palaces in order to enhance the SPL formation. The best star is arguably 紫微 Zi Wei (The Emperor) as it brings mental foresight & balances the aggression. The 4 Transformations are also key.
There are also many other auspicious formations that can indicate success as well, but the process is slower & steadier. SPL's success is a lot more turbulent.
A few things to add about 7K. In ZWDS, 7K is the 2nd most turbulent among all 14 stars. (The most turbulent is Broken Soldier.) Also, 7K likes to stand alone in its palace without the presence of other main / assistant stars. Any other star(s) present in the same palace would have little effect on 7K as their qualities would be suppressed & overwhelmed by it. Kind stars won't help much. Fierce stars won't threaten much. At its brightest, 7K can still succeed even with Hua Ji, but only after much effort.
(Note 1: 7K does not undergo transformation whatsoever. However, it encounters Hua Ji only when another star is present with 7K and is indirectly afflicted.)
(Note 2: According to the classics, the worst star that can pair up with 7K is arguably 廉貞 Lian Zhen. Lian Zhen is translated as 'Purity' or 'Chastity' - which is an irony as it is arguably the most 'evil' main star among the 14 main stars. Both combine to form 杀拱廉贞格 or 贞杀同宫格. There is another name given to this formation: 路上埋尸, translated as 'Roadside Buries the Corpse'. However, there is some controversy over this name as modern practitioners do not think this formation is as inauspicious as it sounds.)
