I am planning to get 3 separate vCenter licenses for them since they need to manage their pools separately. Is that a correct call?
Nope. You add their servers / VM's to a pool. Give them rights to their pool (or server). vCenter can manage 200 ESX hosts and like 5000 VM's, even from a VM, so you only need 1 vCenter license.
If you want to waste your money on more vCenter licenses, that's up to you, but you don't need it.
One of the 3 engineers need to use VDIS and Storage VMotion. So I am planning to vSphere Enterprise Plus license for her. Will this be license be associated uniquely to her vCenter or can I use this license on multiple ESX servers for all 3 engineers if needed in future (even if they use different vCenters)?
License is PER ESX host, vCenter doesn't care. It only needs a vCenter agent to MANAGE the ESX host.
The license requirement says 1 Processor or 12 cores. Does that mean that I can use this license for 1 ESX system with 12 cores or 12 ESX systems with single core? Or any combination?
Licenses are PER socket. Doesn't matter if you have 1 core socket or 12 (but I thought the current license was limited to 6 core, after that its 2 licenses per socket). You buy 2 licenses (assuming 2 sockets) per host. There is no mixing and matching.
