Code blocks, examples, prose, etc can be done a number of ways, two ways are shown below, see the source code of this document to see how these are done. In-line code.

An example block.  

% A matlab code snippet
  for i=1:n
    a(i) = fact(i);
  end

Orgmode has it's own syntax for including figures.

To include a mathematical formula in-line using org-mode, just use normal latex syntax. Here is some in-line math a = α × β. For latex equations or displaymath just type them in the file as usual:

Lists work out of the box (enumerated or itemize).

An enumerated list:

1. Just write a Markdown document, and sprinkle your LaTeX code snippets in between.
2. Save the document with an .md suffix.
3. Run the Pandoc conversion:

A bullet list:

• Just write a Markdown document, and sprinkle your LaTeX code snippets in between.
• Save the document with an .md suffix.
  • nested list
• Run the Pandoc conversion:

Hugo is limited to simple tables, org-mode provides much more flexibility.

Here is a table using org-mode, followed by the code. Second row shows some fancy stuff you have to do to get horizontal lines in a table. The org-mode people evdiently don't like horizontal lines. See Orgmode manual: Column Groups

Does text after table help the bottom rule to show up in some browers?

You can get org-mode to produce your table of contents quite easily, you just have to put the following, #+TOC: headlines 2, on the line right after the #END_EXPORT command in your Hugo configuration sections at the top of the file. The "2" refers to how deep you want the table of contents sectioning.