Is it correct that Hypervisor Free will only support 1 Physical CPU with unlimited cores?
Effectively no point in adding an additional physical CPU to a server if you require to continue using the free version of Hypervisor.
To increase physical CPU to 2 I would need to purchase the VMware vSphere Essentials Kit?
Though there is no limitations on the physical processors free ESXi would support, You can use server with any number of CPUs with any number of cores to deploy Free vSphere Hypervisor (ESXi). But it supports only 32GB of memory.
Number of CPU sockets are not limited in ESXi 5 free version, in Essentials kits the limit is 2 CPU sockets per host.
Though there is no limitations on the physical processors free ESXi would support, You can use server with any number of CPUs with any number of cores to deploy Free vSphere Hypervisor (ESXi). But it supports only 32GB of memory.