Bro, do you know the difference between militaristic assets and assets like poneglyphs?
When Kaido says he'll have the Tobi Roppo meet Linlin at the beginning of Onigashima it means that they get to meet her in person as allies FOR THE FIRST TIME. It doesn't mean Big Mom wasnt aware about them beforehand nor it implied that they didn't talk about their officers in that whole ass week.
The poneglyph thing is an even worse argument because it has multiple possibilities and yet Oda chose to explicitely show that Kaido doesn't trust Linlin about that. That is even more fuel to the fact that they have general info about each other, not specifics!
About the King thing: SHE COULD HAVE LEARNED IT DURING HER TIME AT ROCKS, JUST LIKE WHITEBEARD
SHE CLEARLY TALKS WITH KING AS IF SHE'S JUST CONFIRMING HIS PRESENCE AND THUS THE SURVIVAL OF HIS SPECIES
LMAO at your reading comprehension of a ZKK speedreader