To the installer error messages you're seeing, you may be running into an issue with an older El Cap installer whose certificate has expired. Check to see the date on the installer, if it's before 24-Oct-2019, that can cause the "it may have been corrupted or tampered with during download" message. See https://tidbits.com/2019/10/28/redownload-archived-macos-installers-to-address-expired-certificates
Check https://mrmacintosh.com/how-to-download-macos-catalina-mojave-or-high-sierra-full-installers if you need to download a refreshed installer. Mr. Macintosh has links that point directly to Apple's servers.
I think @dempson hit it on the head with the USB 3.1 compatibility. I just created a macOS 10.11 El Capitan VM from the freshly downloaded "Install macOS 10.11.app" installer, I did find that the VM was created with USB 3.1 compatibility for the virtual USB controller. It exhibited the same kind of "connect a Bluetooth" keyboard and mouse behavior (alternating between graphics of the power switch for both mouse and keyboard". Powering down the VM and switching the USB compatibility to 2.0 fixed the issue and the install went normally. My guess is that a moved VM may have defaulted to USB 3.1 since you're now running it on hardware that supports USB 3.
Regardless of the "official" status in the VMware compatibility list, El Cap does install and run.
