Katarina and Vayne question

In a few recent games, I had a few questions about the two champions in the title. Starting with Katarina. I was top lane with Jayce and for whatever reason, they had Katarina up there. This screwed up my plans as Jayce and it didn't help they were Mastery 7 (Found out once I died...), but they killed me as early as lvl 2. This is what happened, they threw their dagger at me then dashed to it. They then dashed in front of me to keep attacking and when I did manage to get away, they dash again to me and killed me under the tower with them getting away. How can they do that if the dash is on cooldown for not picking up a dagger? Second being Vayne's Condemn. I had a Nasus chew me out for not using it but the thing was, I did but the enemy flashed straight back to me and killed me. Yet the enemy's Vayne stunned one of our teammates... why is that?
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