How I can brand search results page in SharePoint Foundation 2013? I have brand other sites using custom.css file, however it dosen't work in search result page at all. What am I missing here? How I can change background etc?
The search results page exist in a search template/web part. You can edit these and even create your own based on the standard templates.
To see all the default search display templates,
go to Site settings --> Master pages and page layouts. In the Master Page Gallery, click Display Templates --> Search.
The following diagram is how it all hangs together.
The following blog post explains it all in full detail. The 2nd link is how to specifically create your own.
Make sure your css is loaded by the master page. You might have to set it again if your search is hosted in a sub site.
The search page layout can differ a lot from the default SharePoint layout. You might need to redo a bunch of the styling.