add 'Working Papers' Section (within publications) to hugo-academic site

Answering your first question: I don't think this is possible in the current version of the academic theme. However, what you can do, is to use the publication types that are defined in the config.toml file. In this file, there is a list of publication types that are used to categorize publications. It includes a type called "work in progress". You can also add your own publication types to this list, like so:

  publication_types = [
    'Uncategorized',  # 0
    'Conference proceedings',  # 1
    'Journal',  # 2
    'Work in progress',  # 3
    'Technical report',  # 4
    'Book',  # 5
    'Book chapter',  # 6
    'working paper', # 7
    'peer-reviewed' # 8
  ]

For each publication Markdown file, change the publication types parameter to the wanted type, e.g. publication_types = ["7"] for a working paper. The effect is visible when you click on the "Details" link for a publication listed under "Publications" or "Selected Publications".

Answering your second question: to delete a section, delete the corresponding Markdown file from the "content/home" folder. Alternatively, move the unwanted Markdown file to a new folder, e.g. "_not_used", in the "content" folder.

Update: OP found the answer himself, and I am putting it here for future reference:

I found the solution, all I had to do was duplicate the publications.md file, naming it publications_working_papers.md, publications_book_chapters.md for instance. In each file use widget = "publications" and adjust the publication_type accordingly. And also the weight to determine the order.