Updated March 14, 2017
The web browser is displaying errors when opening the WHD Web Console through HTTPS with self-generated certificate.
WHD works as expected. The certificate warnings shown by web browser are correct: self signed certificate does not have Root CA. Connection is encrypted, it's just web browser telling you that it can't establish where the certificate came from. So basically for self-signed certificates web browser will always warn you.
To avoid warnings, the certificate must have proper certification path. So you either use public CA and buy certificate, or use local CA (for example installed on Active Directory server) to generate certificate.
In first case, no additional steps are needed: just install CA reply and everything will work. In case where you are using internal CA, you still have to install Root CA certificate on all workstations. This will tell web browsers (except Firefox) where the Root CA for webhelpdesk.local is. Firefox is using built-in certificate store which is independent from the OS.
Installing Root CA can be either manual (import certificate into Trusted Root Certification Authorities), or by using group policy.
If you don't want to go with Windows CA route, you can use OpenSSL to create your own CA. In that case you still have to distribute Root CA cert to all clients/web browsers. Here's more details on it: