Yes, it is free. Imago is open source under the MIT or Apache-2.0 licence, your choice. It needs no account, no cloud service and no subscription, and it sends no telemetry.

Where are my photos and edits kept?

On your computer. Your library lives in a folder you choose, by default ~/Pictures/Imago Library. Edits are non-destructive, so your original files are never touched. The catalog is a log of human-readable operations that you can back up. Use File > Back Up Library… to make a backup.

Which systems does it run on?

Imago runs on Windows, macOS and Linux, and in a web browser. See Install Imago.

Is it finished?

No. Imago is in alpha. Some things from a professional photo organizer are not there yet, such as on-screen HDR display, video and the Print, Book and Map modules. The project's roadmap lists what is missing.