Username and Email fields are both already unique. There's also a built in username checker that you can turn on within CB > Configuration > Registration and enabling "Ajax Username Checker". The only reason to use CB Query Field is for a more customized check or error display.
As for the query field results your site has errors or something is forcing changes to the buffer or header. Check server error log for notices, warnings, or errors. If you see any then they need fixed. If they output to buffer (e.g. echo) they will break the JSON response. It's similar to why CB Gallery photos would not display for you. Will look into clearing the buffer for next release, but your install should not depend on ajax endpoints having to do this.
forge.joomlapolis.com/issues/5194