There is no difference if you put it all together in one file/declaration or in parts - it is the same - so you can reference any property, field or method from any of the parts
you have not multiple classes with partial. it is one and only one class - it is only the declaration of this one and unique class that is split in several parts
If you want an interaction you need two instances/applications and one has to run in the context of the current user which will communicate with the service and do the interaction with the user