Re: While adding the ESXi host in Vcenter, the host shows as disconnected and grayed

In this case I'd recommend you setup a DC with a DNS server to have a "real life" environment. Take a look at e.g. Building the Ultimate vSphere Lab for a great example.

You either need to use a DNS server for name resolution or add the hosts as well as vCenter Server to the hosts file. On the ESXi hosts this is /etc/hosts, on vCenter Server it's C:\Windows\system32\drivers\etc\hosts.

Sample:

192.168.1.10     vCenter     vCenter.yourdomain.local

192.168.1.11     esx1     esx1.yourdomain.local

192.168.1.12     esx2     esx2.yourdomain.local

André