No, you will just need to download OpManager. The VMware Monitor is built-in with the product but to use it after the evaluation period, you will need to purchase an appropriate license.
Yes it is supported. The following servers are supported out-of-the-box: vSphere/ESX4, ESK4.1, ESX4i, ESX 3.5 and ESX 3.5i servers.
Yes, VMotioned VMs are automatically mapped and reported against the latest ESX servers they are present in.
The SNMP-based data got directly from the VM instances will not also be as accurate due to the intervening hypervisor layer that manages resource allocation over VMs. And, VMware does not expose data via SNMP in the ESXi servers. Also, for the other ESX servers, the minimal data thus obtained does not justify the tedious configurations that one has to go through to get SNMP working.