Hey Gabriel,
I’ve found and eliminated the cause of the different positioning of the header in Firefox: please download this archive, unzip it, and upload into the theme folder (/wp-content/themes/Ikebana/).
Regarding the background image – the current positioning is fully automated according to the CSS guidelines; the specificity of the “cover” background-size rule is that is aligns the top and left of the image with the element (in this case, the page); there are unfortunately no automatic CSS rules to tell the background image to align to the bottom corner and still fit the screen.
Sincerely,
Andrew / Satori Studio