- you can edit your place header in admin menu, just select new header (cover) image with or without viedo and the map will move automatically on right widget side.
- Thic can be done in php, it has been discussed here already, just search for the article and follow steps in documentation, this can be done easily.
- already answered in no.1. But if you want to replace map for a visual banner in homepage, you can use revopution slider for that and create your own slides to replace the map. Map setting can also be found in main wp menu under “Engine setting”.
Hope this will help.