Hello,
1) Fixed header height is changed. Custom styles you can find in child theme style.css
2) You can do this via Theme Options http://prntscr.com/iite39
3) Fixed
4) Done. Custom styles you can find in child theme style.css
5) Use cache plugin, optimize images (https://tinypng.com/), disable all the plugins that you don’t use because every additional plugin slows down a site little bit.
Regards