Where are my answers actually stored?

Nowhere but this browser, on this device. Nothing is ever sent to a server. That's a deliberate choice for your privacy, not an oversight, but it means your answers only exist here unless you move them yourself.

Can I use this on my phone and my laptop?

Yes, but it takes one manual step. Think of your answers like a small file you carry with you, whichever device has the most recent copy of that file has your latest work.

What if I want to keep working on both devices?

Repeat the trip each time you switch. Finish a session on your phone, tap Export, email or AirDrop yourself the file, then Import it on your laptop before you start there. Coming back to your phone later means exporting from the laptop and importing on the phone again. There's no automatic two-way sync, it only moves when you move it.

What if I forget, and answer things on the "wrong" device?

You won't lose anything. Importing merges answers in rather than replacing what's already there, so an older file just fills in whatever's missing instead of overwriting your newer work.

Where do I find Export and Import?

Bottom of this sidebar, right below the print button.