You will need to power down the server to adjust the CPU unless you have enabled Hot-Add of the CPU.
The best place to do this is via the vSphere Web Client or vSphere Host Client rather than the C# fat client.
Windows 2012 should be fine with the change in the number of CPUs but in case you're worried about it, backup the VM first (if you have capacity to do so).
From my experience with Windows 2012R2, I wouldn't expect issues with increasing the number of vCPUs.
I'd suggest you just try it. In case it doesn't work you can always reduce the vCPU count again.
"Now I want to see if I can adjust the amount of CPUs for this VM to the maximum."
Best practice is to assign resources as required by the guest OS. Remember that increasing the guest resources will also increase the overhead on the host, i.e. the host may require more resources than necessary to handle the guest.
What are the possible things that could go wrong increasing vCPUs that I should be watching for?
This is a media streaming server which will require excessive use of CPU.
2 CPUs at 10 cores each = 20 cores. 4k steaming will require high CPU utilization.
What would be considered a safe increase?
If something goes wrong with vCPU increase how would I know it?
When increasing amount of CPUs what are we actually increasing?
Lets consider the following scenario:
Processor Sockets: 2
Cores per socket: 8
Logical processors: 32
Also if I use vSphere client to change CPUs it allows me to change :
Number of virtual sockets: 2
Number of cores per socket: 2
but via web browser it shows:
Cores per socket: 1 which i can't change
and the only part I can modify are the 32 logical processors
Please kindly advise...