For the featured image, you can use Page Header addon.
1- Active you Page Header addon and follow to your homepage, there you’ll find a new metabox ‘Page Header’.
You can set a background image and for the Content tab you place your text. For the parallax just mark the option “Add parallax effect to background image?”.
For your Blog page, go to Appearance > BLog Page Header
2- For the navigation just go to Customizer > Layout > Navigation Position > Float Right