How do I get scrips?

[Niwashi]

Where does it actually say the current time in Eorzea?

Clicking the on-screen clock (top right of the screen unless you've moved it elsewhere) will toggle it between showing Eorzean Time (ET), Server Time (ST), and Local Time (LT). Since server time isn't really useful for anything, and your watch can tell you what time it is locally, I'd recommend keeping the on-screen clock set to showing Eorzean Time.