Good enough earmuffs likely stop it. The second years had them for the babies. So, either the muffs are enchanted or being deaf makes you immune.
Basilisk is a similar thing, killing everyone who looks sees its eyes and paralyzing or turning to stone any one who indirectly sees its eyes. Taylor... I feel she'd be able to see it through bugs. They're not looking it in the eyes and even if they do... Not her.
That sort of thing was noted. Few things are any sort of foolproof, and even a very average witch or wizard who only did okayish in school is likely to have all sorts of counters and protections that they could employ against a vast variety of problems. That doesn't mean that a given measure for Skitter-ing enemies can't be useful regardless; if a way to deal with something isn't actually used, the fact that it
could, however easily, does nothing to change the results.
As far as the specific subject of basilisks are concerned, though, that seems something that might just never come up. They're very good at killing, which could be useful, but I think Harry and Taylor would end up deciding against it if they were considered. Whether or not there may be something complicated in the incubation process and whether or not it could be figured out, there's some degree of time investment required before a viable product is available for use, for one. Further, there's a lot of ambiguity that would be tricky to test and high-stakes when basilisks are indeed so lethal; Harry might be able to employ magical murdersnakes very well, possibly, but Voldemort may or may not be able to seriously compromise that for similar reasons, raising questions about what might result of two different parselmouths involved as adversaries, and the enemy one possibly more capable on some way that might matter, plus Harry's accountings of the last basilisk that he dealt with puts a worrisome uncertainty as to how safe it'd be to see through bugs when basilisks seem to have
seriously magically potent gazes with very consequential effects happening to people who saw it indirectly and one that saw it directly, yes, but was a freaking
ghost and still got hit hard by it. All in all, it comes across as something that Harry and Taylor might likely evaluate as just not promising enough to pursue.
More reason to be trained. Imagine Harry being clumsy and cutting himself with his own sword. Unless Fawkes' tears makes him immune even 3 years later... He's dead.
Plus, with magic he could maybe do some Jedi shit. Throw the sword at a foe and summon it back. The summon might get them.
Swords do take considerable time to learn to use well, and a whole hell of a lot of work. Still, there could perhaps be ways to work around such requirements with magical assistance somehow, and if Harry could just get some hammerspace pocket or whatever to keep it in, Gryffindor's could be something that'd just be nice to have; it may not be some amazing solution to everything, but being able to whip out a sword when convenient sure would be convenient.
One of the significant considerations regarding any kind of intentional employment of the basilisk venom, though, would be motivation. Gryffindor's sword could be very handy for dealing with some perceivable key issues, but actually being aware of such a need and the possibility of the sword to address such needs are prerequisites. That said, Harry and Taylor do appear to be on the right track.
They were able to
guess and put together a reasonable suspicion about the significance of the diary horcrux, how mattered, and the existence of other things like it. Harry also of course knows how he dealt with it. They might not know just how and why basilisk venom in particular is something that is amongst the precious few means of destroying their expected hypothetical targets, but Harry does know that the diary didn't seem fazed in the slightest by any prior mistreatment and stabbing the book with a basilisk fang worked great; maybe that was some property of the diary being mundanely fragile in the face of jabbing it with a big ol' tooth such that something hardier even without magic being involved might not care, or maybe the ludicrously lethal magic of basilisks is just that potent, but it's a very solid start.
Conveniently enough, too, though the imbued sword might circumstantially be troublesome to get or keep, Harry and Taylor could perfectly well do as Ron and Hermione do in canon and just go back to the source. The corpse is still down there, full of teeth full of the special venom of absurdly fatal doom, and it's viable in canon at least up to a later point. Perhaps more importantly, too, regardless of any aims for using basilisk venom specifically for dealing with the lich guy's phylactery things holding his soul, Taylor could entirely reasonably just want the venom for poisoning people.
If Harry tells Taylor about his second year, as could easily well enough happen, particularly for the significance of the diary, Taylor might pick up on there being an effectively untreatable fatal poison that she could get her hands on. Alternatively, she could make discoveries when doing some very basic research about dangerous things that the Wizarding World has to offer, and one of the most prominent ones within that, which could itself dovetail into Harry talking with her about it. Taylor having any sort of inquisitive aspirations about maybe acquiring basilisk venom somehow could very straightforwardly result in her learning that it is in fact possible and simple. From there, Taylor's trick of using sacrificial bugs and others to ferry them or otherwise just put venom somewhere consequential could give some folks a very bad day one way or another.
Taylor: It's because the Wizards suck at math and refuse to improve?
Goblins: ...Yes.
The currency really is just utterly senseless. It's... perfectly wrong, basically, difficult to actually be any worse. It comes across as one of those things that is intentionally quirksome for the setting, but that doesn't make it any less ridiculous. Prime numbers don't care about ease of calculation; they don't divide regardless. They're the exact opposite of ideal. However much a quagmire the muggle coinage system may seem at a surface glance, it's based on highly composite numbers, ones that have more ways of division than any preceding values.
How much is something worth half a Sickle worth?
Too bad, can't be done unless physically cutting coinage into fractions, which doesn't seem to be a thing in the Wizarding World and has goblins offering a compelling reason why. How much is half a pound worth? Well what combination of coins do you want, because there's all of them! And if the thing being valued could be itself divided up,
no problem. A third of a dozen eggs or something? Can do, there's coinage neatly applicable for thirds and dozens both, as well as in between, and they combine into larger coinage evenly with several of them. There are even half-penny coins that are whole and two-penny and three-penny coins for all your division needs! ...but no, the Wizarding World has to be "different."
That was what I was hinting at. Seriously Dumbledore just planned to let Harry pick it up without a sheathe after he died in Canon, that was beyond stupid.
Fawkes outlives Dumbledore. I am now imagining a thoroughly bedraggled-looking phoenix run ragged covertly keeping an eye on Harry at all times after Harry gets the sword, and being frantic with worry that the worry itself will lead to a premature burning at just the wrong time to wind up with Harry ever so slightly nicking himself and keeling over dead. Hidden behind any tree could have been a baby phoenix in a pile of ash who hasn't gotten a wink of sleep in weeks. Truly, Fawkes is the unsung hero of the story.