@victoralejandrobr : You can have a video header on Homepage. To enable it : Go to Appearance => Customize => Header Media
Under Enable on : Select Homepage /Frontpage.
The featured image will be displayed above the post if you enable it from the customizer but the image will not appear in the header. Make sure that you have added featured image on every post. To enable featured image on each post. Go to Appearance => Customize => Theme Options => Layout Options
Under Single Page/Post Image : Select enable.
Let me know if this resolves your issue.
Regards,
Tikaram
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