Hi,
Colors issue
The issue with the colors is that you have a lot of custom CSS forcing a white background color on the search. I changed everything on the theme options to transparent, now if I remove the custom CSS, I get this: https://i.imgur.com/Uc21ANm.png
I am not sure if that is a good option though, as it will hover over all of the items in the menu, and because it is transparent, it will not look very nice with the underlying layer.
Instead maybe using this custom CSS you can change the background to white, whenever the search is opened:
.asp_m_1[asp-compact=open] {
background: white !important;
}So it looks like this when closed, and this when opened.
Search issue
The redirection issue might be caused by other search plugins – please make sure to deactivate any other search plugins, so that they don’t override each other.