Can't Medaka's "The End" deal with Rick's intelligence?
That's Bookmaker. It should be able to if she uses it.
conceptual manipulation gg rick is dead
What does she do with it, can it kill him on a 2-A scale?
MB's conceptual manipulation comes from All Fiction erasing colour, and from a statement that it could erase the concept of time. None of it's on a 2-A scale or could be reasonably argued to nuke Rick.
From the looks of it, I don't see Medaka using her powers to mess with Rick's means of resurrection before the latter may die some times, get a read on her from afar and then stop her in time, possess her or nuke her timeline.
This does seem a bit plausible actually. Medaka often lets her opponent get the first hit, but if she so much as blows in Rick's direction he'd die, and she'd likely do that before she gets to her incap hax.
However, Rick can't just "nuke timelines". He can create them and merge them, he can't just travel to another timeline and nuke the original one. He can eventually nuke universes, but Medaka could resurrect from that, although it's hard to tell what'd happen from there (if she'd be able to bring the planet back, if she'd be able to do anything in space, if she'd be able to travel to another timeline).
The profiles a bit unclear, but does Rick's possession even work on beings that aren't other Ricks?
Also, given the stuff we've seen from Rick, idk how in-character that series of events would be for him. He doesn't just timestop and kill everyone even when that would be easier; he doesn't like using it. And if we were assuming hypercompetence, Medaka would easily win.
Can either kill each other is the question?
I'd lean towards no, but I'm not sure how Rick's resurrection would interact with EE. Doesn't it require his consciousness to be sent off to another cloning machine? If he's EE'd that wouldn't be able to happen. So if this can get around it, Medaka would be able to kill. And Medaka doesn't have self-sustenance, so she might be able to be killed if the planet's blown up.
But still, even if they can't kill each other, they both have a wealth of ways to incap. Rick can BFR, mind erase, and freeze. Medaka can body puppetry, mind manip, disease manip, book maker, and decrease intelligence.