On Cassiopeia's counters:
Yorick does NOT beat Cassio. Neither does Graves unless she literally throws the game away. Kayle I'm unsure; I suspect she doesn't either. Soraka is about 50-50, Mordekaiser is about 50-50 with spellvamp runes (if Cassio does not have spellvamp runes, Morde with spellvamp runes wrecks her). Skarner used to be a problem, I'm not sure how it is now with the Q mana issues. I suspect it's still very hard. Riven should be good although I've only seen one successful Riven against my 1600 queue partner's Cassio. Vlad might also be trouble with spellvamp runes, don't have a lot of experience there. Urgot is a hard matchup for equal skill, but if he outskills the enemy he can still do it. I've seen a Renekton that beat Cassio too although I think that was due to a lack of understanding on the matchup and not actually that Renekton beats Cassie.
The main counters to Cassio are anti-caster assassins, eg. Leblanc, Kassadin, Talon. I think the Talon matchup is very winnable for her.
I also have some theories on AD bottom lane carries, in particular Caitlyn, Sivir, and MF. Sivir has some wonkiness (spellshield does not do anything to Cassie W) so I'm not sure about that; MF I have no experience so it's more of a theory thing. Caitlyn is probably a skill thing, but I think she can do it.
Pretty much everyone else loses badly.