Thank you so much Heavy, both for your efforts and details.
I have done all as you suggest (and mentioned it in the post number 5) but still have the ERROR message:
Agent exited with code 1: Cannot login to vSphere Server (reason: [500] Internal Server Error). Please check the credentials.
Here is setting defined in Setup → Agents → VM, Cloud, Container → VMWare ESX via vSphere:
Which format the username should have?
domain\user or just user or user@domain or it has to be local user?