You can enable administrative access in the Preferences window: Check the option List all users. This will cause WhatsOpen to prompt you for a username & password for administrative access when you list files.

This administrative access runs the command lsof as the root user to give you a file listing for all users instead of only the logged-in user. It has potential security repercussions and is disabled by default both for convenience and practical security guidelines.

Yes. Open the Keychain Access app and create a new Password Item with cmd+N. Enter "WhatsOpen" as the name, along with your username and password, then click Add. Next time you use What's Open, you'll be asked to allow the app to read the data from Keychain. Enter your password and then click on Always Allow.