Grimoires go to Grimoire Heaven till next candidate able to wield them is born. Asta's is dirty and tattered because, because of the demon dwelling in it, it was not allowed in the G Heaven . U_U
Or maybe the 'demon' didn't die and was only imprisoned in the sword so the grimoire couldn't vanish and return to the library and that's why it's so dirty and tattered- lying in the ruins where demon's physical body lay wasted. When Asta came near it, it found someone who could wield it again and came to him. Or the elf elder soul decided to give it up to Asta recognizing his spirit.
Yuno's pendent + 4clover and William showing special interest: " we need him to grow stronger"
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About Licht's comment regarding manna : Elf Elder may have been been able to master the swords and demon residing in it fully to not affect him negatively. In contrast Asta is able to wield them simply by not having any magic but physical strength only.
As for the swords - they ought to be a set but the grimoire comes with single inscription only, so may be Asta needed prove himself before getting the whole set? Magic emperor probably guessed that Asta could get hold of the second one. Though I may be giving him more credit than he deserves, still he knew that they would be facing stronger opponent but didn't send backup. Later on most of the treasure was lost but the wind spirit or sword that Asta picked. Yer he seemed satisfied with the outcome.
Clover kingdom is certainly at a main party of the conflict- the demon's skeleton is in it's border village. The sword was again in a border side village so was one of the stones. Licht implied that his conflict was with Clover to which Yami won't understand being a foreigner.
Maybe elves do not die just because their bodies die and spirits can move to new bodies and William was able to fool Yami because he was not channeling Licht at the time.
We know- grimoire comes with a single magic and rest of the pages are filled only if the mage is able to advance or gain ability for more spells. So it may not matter whether Yuno's 4 leaf is counter to Asta but that he is developing it specifically with Asta in mind that it may become the counter part in some way. But of course, it may also be the aura of the first elder. Then there is his pendent with special design.
Licht may have been right that the humans attacked elves because someone influential was either jealous of them or Licht in particular (the kind of Clover kingdom?) or afraid of their power. The elf leader lost to the demonic side when fighting back in anger and demon took over his body with full transformation or he summoned it even at that cost- leading to the first magic emperor facing him and sealing him back in his own sword or killing him in the process. That may also be the reason why Licht felt the betrayed so badly- his friend was the one to finish his dear master t save humans.