Since Katarina is now one of the most mobile champions in the game

No, if anything, that should be the last thing to go because it's thematically tied to her kit (think TF card mechanic). Also Yasuo is still more mobile.

No, she's mobile because she's melee, squishy, has no cc, and cannot reasonably itemize Grievous into her build.

I don't think they'll do that, mainly because it's supposed to be a kill for her and not something you can just heal up as it kills you

Katarina has like 3~ different ways to go in and about 2 different ways to get out ( one of which requires her to plan on getting out)

people keep throwing out the word mobility like anything that cause you to move is mobility ( which by definition yes but game wise no)

Kassidin and talon are by far the most mobile champions in the game as they have accesses to their mobility at almost any time without any real hindrance/cost. (yes kassidins jump can cost a lot but assuming he hasnt blown all his mana for no reason and he needs to GTFO he can)

Targeted mobility that is to conditional or requires considerable set up isnt considered high mobility( which is why leesin is coincided extremely mobile but someone like sion isnt)

Katarina is mobile, but no where near so where she should be balanced around it.