"Is this a mandatory requirement to have such dedicated switch for QinQ and all of my other Network/Server's VLAN to be separated from it?"
In many cases the answer is no. This would depend upon your SP and the service they are providing you. I would think in this case you would want a pure L2 service, basically the equivalent (or actual) of 'dark fiber', which means what ever you send just gets passed through unchanged.
Therefore you EX4200 <--> EX3300 connection is a tagged link which has your server VLAN as a member, most likely.
I'd suggest this conversation is something you have with both SP and whomever you purchased your Juniper equipment from. If gray market purchase, then you would (and should) be on your own.