You can find new skills by Exploring the City Ruins or through Officer Recruitment.
- Always dismantle the officer skills you don’t want, they provide twice the XP books
- Change your officer setup and the skills they have depending on what you're doing
- All Purples isn't always the best choice
Yes, it depends on two things: The level of your Officer and their Star level.
Yes. The higher your Officer's level (when you UPGRADE them), the more slots for additional skills will appear.
You can upgrade the Officer Skills by finding/buying more Skill Fragments and fusing them.