tanach - What are the reasons or rules for the different variations in vowels on the Tetragrammaton?

I'm aware that the vowels of the Tetragrammaton are unknown and i'm not asking what they are.

I see a lot of variation in the vowels placed or not placed, on the Tetragrammaton.

Sometimes a hataph patach on the first letter, sometimes a shva, sometimes a hataph segol.

Sometimes a holam on the second letter, sometimes no vowel.

Sometimes a kamatz on the third letter, sometimes a hiriq on the third letter.

I'm interested to know what reasons there are for when it's written with some vowels and not other vowels.. I see a pattern where it is spelt with a yud under the vav, every time it follows aleph,dalet,nun,yud. So it seems maybe there are some rules or conventions.

Examples below

The Mechon Mamre site for that verse has the word with just the two vowels, and the yud with the shva. http://www.mechon-mamre.org/p/pt/pt26e4.htm

I see in bibleworks the cholam

I see it seems maybe every case of aleph,daled,nun,yud followed by yud,heh,vav,heh there is a chirik under the third letter of yud,heh,vav,heh

e.g.

and in that Kings example a vav with a cholam

Answer

There are kabolistic ideas in different nekudot of the Name see this.
(See second line from the bottom (and footnote 25) here)

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But the way I was tought all the examples you bring are just ways to hint to us how to read it

Most of them are hinting (having very similar nekudot) to Adonoy
in the the last 3 examples they are hinting (having very similar nekudot) to Elokim

Not always are they exact:

The shva is a hint to the hataph patach and to hataph segol, depending on the rest of the nekudot.
The holam is sometimes skipped

Since the nekuda on the 3rd letter is enough for the hint

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There is mishnah Berurah that when you imagine the name before you at all times it should be with the nekudot of the word fear
Source mishna Berurah 1.4

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Edit
another reason of the 2 versions when it is pronounced Adonoy

shulchan aruch harav 5.2

When, however, [the name] is written as י‑ה‑ו‑ה, there are those who pronounce the alef with a shva, for this is the vowel of [the corresponding initial letter which is] the yud of the name י‑ה‑ו‑ה. Others pronounce the alef with a chataf patach, using the same vowel as the alef of the name A-donai.