Welcome to the Community,
it's indeed the free license you are using "VMware vSphere 5 Hypervisor". Unless I'm mistaken you can use the same license key on any number of hosts.
- Just enter the license key, see http://kb.vmware.com/kb/2014295 (Licensing a standalone ESXi host)
- You need to copy all the VM's files, not just the .vmx file. The .vmdk files for example, are the VM's virtual disks. Depending on whether the virtual disks are thin or thick provisioned you can use 3-rd party tools like Veeam's FastSCP to copy the files. You can also backup and restore the VM's using e.g. Trilead Explorer.
- Afaik you can use the license on any host. You are only limited to 32GB physical memory on each host.
André