ok, i somehow glossed over your question on permision to use this. yes, you absolutely can, though keep in mind that it was created by a human in a rush during their free time at school, so it might have a few errors.
The internal order is Normal Fighting Flying Poison Ground Rock Bug Ghost Steel Fire Water Electric Psychic Ice Dragon Dark Fairy (Stellar), mostly remembered as a remnant of separating physical and special types for the split, but it is still visually referenced in a few places like the Gen 3/4 Pokedex search options and Gen 8/9's order for type searching in the box, which is where Stellar can be seen as well.
Of off immediate memory I can confirm this is the same type order that's used for the TM crafting menu in Scarlet & Violet, as well as in a number of spinoffs such as the Ranger trilogy (excluding Fairy in that instance since it didn't exist yet, of course). Something worth noting here is that for most Types in this order, their order placement may have been loosely based on their individual matchups against the others: every type from Fire (Type #2) to the Flying (Type (#10) as well as some others can be viewed as such.
This one seems the most accurate since the two most optimal types, bug and rock, are right next to each other.
most special attackers with ice beam will run ice beam. it is fairly common.
eh, idk if that's true. Ice is simply not that great coverage on things without STAB on it; it hits a lot neutrally, and some key things super-effectively, but doesn't synergize well with a ton of things, enough so that most things with it won't run it actually. Out of all OU mons with ice beam, the only pokemon with a set with the move is Kyurem, which gets stab on it. Out of the entirety of the game, if you look at all the pokemon that reliably run ice beam that don't get stab on it, you begin to see a pattern: It's a lot of water-types, such as Inteleon or Milotic, or pokemon that viably run BoltBeam, like Arceus-Electric and Porygon-Z. Most other Pokemon that get Ice Beam simply have better options. In this aspect, I don't see how it's so different from, say, offensive psychic types running Focus Blast, other than the fact that there's a lot more and better offensive waters than offensive psychics. I think the confusion here is mistaking ice STAB for ice coverage. Ice STAB is incredibly useful because it's resisted by very little and hits key threats hard, i.e. meow and weavile in OU. Ice COVERAGE is not that useful because, while it does hit some key threats hard, it lacks power to back it up, meaning you don't just run it willy nilly without something in particular to hit.
ice synergises really well with ground, and is very frequently coverage. there is a reason ice fang is considered a useful move despite being a terrible move.
proved is a strong word. you definitely did not prove that
What pokemon actually runs ice fang? Like, the only one I can find is gen 5 gyarados.
mega aerodactyl and mega sharpedo used to run them, at least in randbats, but only because both of them get boosts on it; Aerodatyl gets tough claws to boost it up to an 84 bp move and sharpedo gets strong jaw to boost it up to a 97 bp move.
Ice and fire types being picked is usually because the pokemon that needed hidden power were either grass or electric types, and they would be the ones to run fire or ice.
I didn't really do a purely numerical ranking. water was that low, because having few weaknesses is not that useful if you don't have resistances as well. its pretty good defensively, but that is not enough to get it higher imo. its good, but there are a lot of good type combos.
