Even if she hadn't unwrapped it, she should surely have asked Arondir what it was and why it was so important to Adar and if he'd told her it was some device of Sauron she would absolutely have wanted to take a look. Also ridiculous that Arondir didn't bother to tell her! One of the biggest plot holes in the season thus far.
Something that I don't recall anyone picking up on is that the way the blade appears out of thin air is the reverse of how the blade of the Morgul-knife disappears, melting and vanishing like smoke in the air. And it working via blood-magic is a suitably gothic touch so in itself it's not a bad MacGuffin, it's just that the plot around it is made of stupid.
To be fair, it could simply be that there was always supposed to be a proper tunnel to Orodruin but that it was never finished due to the war (like maybe they'd done the volcano end and the dam end but not the bit in between), so Adar had to improvise. The idea of causing a phreatic explosion to make Orodruin blow up is really not bad at all, as that's a
real thing that happens sometimes.
The wall o' flaming doom is a real problem though, one of those hits like a freight train: it's literally red hot, it's moving really fast and it's got ash, rocks and rock fragments and even boulders in it, and it's volcanic gases too so it has just so many exciting ways to kill you.
Not necessarily, as Tolkien never made his mind up about what made Orcs tick; there are different versions. It's a bit of a poser philosophically because if they are Childen of Iluvatar then Eru would have to be creating souls just to have them be embodied in Orcs, taking it into Problem of Evil territory as they're born only to suffer and bring suffering to others. (All the more complicated as Melkor had begun as an aspect of Eru's own thought, and though he was a necessary force of chaos all the evil he did was still fundamentally down to Eru himself).
One possibility is that there's only what you might call an original stock of spirits for Orcs and they just get reincarnated. At least then Eru doesn't need to make new ones.