1. Move the main menu so it is down and just to the left of my logo
– do you mean you want to remove the menu?? or you need in this order menu, logo, then cart, wishlist icons?
2. Center text in the white space above the header.
– this is not possible for this type header.
– let me know your site login credentials. so I can try and check
3. Place a static image in the space under the header. No desire to use revolution slider just yet.
– just go to pages > you home page > edit and remove the rev slider element and add the image you want there.