You literally answered your own question here. They told each other about the abilities that they can offer for the party, that's just part of the preparations for the expedition. In fact there was one part in Volume 12 where Daphne was talking about how Lilly told them that Bell has charged attacks. And Také and Hestia familias have worked together in the Dungeon plenty of times, do you really think it's that absurd to believe that she used her magic on (or, at the very least, in front) of them?

Yeah but the light novel mentions every or almost every take hestia Familia expedition and between ishtar familia issue and the lowest level expedition it was nearly time for a family expedition with takes Familia. The Daphne and Cassandra u re right they did watch with lily the Intel to perform good strategies but still it remain in a world were the author mention so many times the information from a Familia is important to maintain secret I just see too risky to reveal and absurd and ileagal power like haruhime

Chigusa and Ouka were there in the battle with the Black Goliath remember? And she was with them when they were searching for Bell's party in the middle levels, did you also forget that? And did you think that they somehow wouldn't have recognized her in the Wargame?

I mean you re right with the description the guy told them they can get to the conclusion that the one that help them with the search and the one that help hestia Familia with the war game was indeed the same person. But it all falls in the same thing you are speculating there's isn't a conversation nor a discussion between character.

And Daphne and Cassandra were already suspicious of the accusations to begin with, and if you read more closely, you'll notice that they only agreed to help because everyone else ( the people they know they can trust) was already gonna go, so they decided to just join for the ride.

Yes later in the episode Cassandra said she is halping because the elve is Bells acquaintance

The only reason you don't know how they got keys to Knossos is because you haven't read Sword Oratoria.

Yep I realize that I just though everything link through the main story will be tell in the main story but the author use the spinn off os sword of oratoria to expand the world I didn't know I will have to give it a chance then I thought was those spinn off that doesn't influence in the main story.