What stays on your computer and how proxy keys are protected.
No. There is no telemetry and nothing is uploaded. The app contacts your proxy gateway, the IP-check service, the sites you test, browser download sources and the signed update feed. See Network connections.
On your computer, in the app's data folder. See Data locations.
It is encrypted with AES-256-GCM in a local vault whose key is protected by Windows DPAPI, the macOS Keychain or your Linux keyring (or a machine-derived key, flagged as Reduced protection). It is never shown again after saving and never written to logs or the database. With WebKit it never reaches the browser process (a local relay adds the login); Chromium-family browsers and Firefox receive it to authenticate to the proxy directly.
Anyone who can log in as your operating-system user can, in principle, use the app with it, so protect your OS account. See Credential vault.
Yes. The files contain no credentials and no personal data; everything is created on first run on each computer. Each person needs their own proxy plan and enters their own keys.
The EXE is not Authenticode-signed unless a code-signing certificate is configured for the release. Click More info, then Run anyway. Update packages are still verified with the publisher's Ed25519 signature; see Updates.