How do I execute 2 animations in parallel?

You can do so by first making the 2 animations a child of a single storyboard as follows:

<BeginStoryboard>
    <Storyboard x:Name='Animation'>
        <Storyboard x:Name='FadeInStoryboard'/>
        <Storyboard x:Name='FadeOutStoryboard'/>
    </Storyboard
</BeginStoryboard>