Question

I understand that ViewModel shouldn’t have any knowledge of View, but how can I call MediaElement.Play() method from ViewModel, other than having a reference to View (or directly to MediaElement) in ViewModel?
Other (linked) question: how can I manage View’s controls visibility from ViewModel without violating MVVM pattern?

Answer 1

1) Do not call Play() from the view model. Raise an event in the view model instead (for instance PlayRequested) and listen to this event in the view:

view model:

public event EventHandler PlayRequested;
...
if (this.PlayRequested != null)
{
    this.PlayRequested(this, EventArgs.Empty);
}

view:

ViewModel vm = new ViewModel();
this.DataContext = vm;
vm.PlayRequested += (sender, e) =>
{
    this.myMediaElement.Play();
};

2) You can expose in the view model a public boolean property, and bind the Visibility property of your controls to this property. As Visibility is of type Visibility and not bool, you’ll have to use a converter.

You can find a basic implementation of such a converter here.
This related question might help you too.