rootkit / keylogger detection

You are welcome. I would try doing a full router reset to try to get it back to 'factory' specs. If necessary, contact your ISP for assistance. Explain the problem and they may be able to reset something on their side. If you can do that, changing the password should be enough.

If no one else has physical access to your Mac then there's no rootkit or keylogger.

If you want to check for malware download and run Malwarebytes. Malwarebytes was developed by one of our own colleagues here in ASC and is about the most proven anti-malware software for Mac.

If you can't find the key logger and you have a backup made prior to someone accessing your computer/router, boot into the Recovery Mode (command - R on a restart), erase the disk, and restore from your backup.

You are welcome.