Was it even possible for the ghost soldiers that were recruited to be killed in battle? It seemed that once they showed up, the battle was over. I did not see one of them die. They could have just used the ghost soldiers and saved everyone else for the battle with Mordor.
shareMostly no, but I think a *bit* yes to the first question. There is, in Tolkien's worlds, a prominent sense that the physical world and the spirit world are separate but intertwined. Some beings seem to have moved from one to the other. Gandalf, for instance (and the Balrog and Sauron, for that matter) is a Maiar spirit but has taken physical form; he still has feet (or whichever spectral appendages) firmly planted in the spirit world, though, which is one of the reasons he is as powerful as he is and can perform magic. The Ringwraiths, on the other hand, were physical beings, but are becoming more phantasmal due to the influence of Sauron and his "gift" rings.
So, I'm guessing that the ghost army - almost entirely spirit-world denizens at this point - could not be harmed by mortal weapons, which is 99.9% of the weapons held by the orcish hordes laying siege to Minas Tirith. The Ringwraiths, however, are more than likely capable of harming the ghost soldiers, but would be grotesquely outnumbered. There might be a scattering of evil, twisted, wraith-weapons amongst the orcs, too, of course. After all, Merry happened to be in possession of just the sort of barrow dagger needed to pierce through the Witch King's "ghost armour"... so it's conceivable that the orcs had a small number of items that could work - but not nearly enough.
I'll take a brief pause to note that the ghost army did not participate in the Battle of Pelennor Fields in the book version, only being recruited to take hold of corsair ships and annihilate the reinforcements thereon to help more indirectly with the fight. That much fulfilled their oath/curse in the literature.
That brings us to the next bit about how they could have just used the ghost soldiers to keep fighting.
First, the closer they got to Mordor and Sauron himself, the more likely it would be that anti-ghost weaponry and magical attacks would be deployed against those ghosts. Second, and more importantly, those ghosts were cursed to help very briefly. They had broken an oath to assist the Kings of old and were cursed to undeath until summoned to help when called by the true king, descendant of Numenor, heir to Gondor, and all that stuff. Their oaths fulfilled, they could then find rest and peace, which they did. They didn't want to stick around, only doing so because of magical force, and left as soon as they could. Think of them as ghost mercenaries where the payment is passage to the afterlife. The contract wasn't to fight Sauron to the end, it was to help with the siege at Minas Tirith.