Solved it! Finally found codes in old threads that works for both problems (transparency of header and invert burger menu on home page), thank you @tuanphan
If anyone has a similar problem, here you go:
Transparent header:
header#header {
background-color: transparent !important;
}
article section:first-child {
padding-top: 0px !important;
}
White burger menu on homepage:
body.homepage .burger-inner>div {
background: white !important;
}
