Can I get a copy of my data?

Yes, at two levels, both from Settings → Account:

• My data on this device: a readable file (compressed JSON) with your places, circles and messages, created on the phone. It holds your own data only.
• What the server knows about me: a nearly empty document, on purpose. It lists your account, your devices and your subscription receipts, and that is everything the server holds.

Both exports are immediate and involve no human operator.