i wouldn't say arya isn't ruthless yet she's still that sweet girl from season one but she's becoming evem more bitter by the day..rmb when she was like : "i can be your family

" but that melissandra and arya moment was like "yep she's mos def on the path of becoming a monster..."..not sure about cat...sure she can strategize but she;s nowhere in tywin's league
No-ones really fukkin with Tywin he has the money and experience. No-ones got the money to outbid him and who ever did have his War experience is dead or far far far away. Hes a like a Medieval Ginger/Blonde Bruce Wayne/Tony Stark type
You forgettin how Arya told Jaqen to go kill himself, if he didnt do what she said. She has a hitlist of people she wants to off, if that aint ruthless

All shes lackin at the moment is the know how to do certain things (due to her age) but the Will is strong in her. That Arya/Melissandra scene, I took that as Melissandra being kind of shook of Arya and that when their paths eventually meet again, someones gunan end up
The Way Cat

Robbs authority with Jaime by helpin him escape. Then before that, she fukked Ned over by takin Tyrion hostage before Ned could get to the bottom of things. She put her own personal agenda above her own flesh and blood power positions and its fukked her King/Son and Husband.