[@Norschtalen]

For your first scenario, it's unlikely. Too close to what the Dark Brotherhood does, and they would not appreciate competition when they already had the Morag Tong to deal with.

The whole issue with your character is that assassinating is not something you can just wing or decide to pick up for the fun of it. She needs to have been taught by someone how to fight, to kill, to protect herself. It's all circumstance and luck in her backstory - and if she just kills for fun, why not be a bandit, or highwayman, or mercenary? Her skillset needs to be explained, not her reasoning. She's clearly a psychopath, that's enough reason for killing.