People of that world can read Japanese.
The manga kind of brushes over it (like several other things), but the novel mentions that the sheer number of influential transmigrators has caused it to be fairly well known.
An actual reason in this case; as mentioned, curse sorcery - "I've told you my secret, tell me yours" to extract information out of them. Not like they're likely to live long enough to tell anyone else about it.
He only just previously ranked up for the last thing he did.
But you're looking at it the wrong way, the rank-up isn't the primary reward for defeating the dragon / fixing the world tree - rewards for those the king keeps trying to give him and he keeps turning down because he's a dumbass MC.
I don't know how much she even talks to the others. Something to note is that rich girl, whom bodyguard DOES talk to, wasn't among the girls ignoring him.
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What would be amazing is if there were actual consequences for the girl who ignored him and the others that believed her, but we know...
MC hates himself, or rather the character that he is, but is obsessed with yuri.
So basically he's completely ok with being treated like trash (and if anything welcomes it, he tries very hard to get the heroines to lower their opinions of him), but absolutely will not stand for anything that...
Corgino had at least been set up as a long-time villain, so him getting immediately crushed would have been a letdown.
Meanwhile the author probably realised no-one gave two shits about these characters; in the novel it's a fight about as long as Corgino's.
...he already furiously hates the MC though.
And not through manipulation. Did you miss or forget the tournament chapter where he got beaten up by the beast girl, and after waking up, all on his own decided the Ark household needed to be destroyed.
Though the age difference is still questionable, at the start of the series she's 13 and he's 18.
At this point in the story they're a bit over a year older than that.
It's nothing to do with lightspeed travel or anything (Imperial ships are FTL anyway); Imperial nobles simply live for centuries or longer. At this point in the story Liam himself is over 60 years old.
They'd have to be gods to NOT be pushovers compared to Helvi.
Unless they have some kind of asspull mcguffin, a fight with someone who can destroy the planet by jumping too hard is not really something a human can manage.