If a subroutine is called within a function, does the function always wait until that subroutine is completely finished before it will proceed with the rest of the function? If so, is there any way to make it not wait and continue on with the rest of function and not care what happens in the subroutine?
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In the normal course of things yes, the calls are synchronous. That is, when you make a call to a subroutine from a function, the subroutine will fully execute and only when finished will execution resume in the calling function.
You need to use asynchronous programming to achieve what you want.
See Calling Synchronous Methods Asynchronously on MSDN for details.