if i wont to create a proxy veeam, that proxy veeam must have the the some OS are installed in nodes ( 2008 R2 Core ) ?
Yep, the operating systems of source and off-host proxy are the same; though, the edition doesn't matter.
is this possible ?
As to the “dirty” shutdown message upon replica starting, kindly, see this
topic that should clarify this situation for you.