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I would continue using the macro. You can use markup inside the macro that expands differently for HTML export than it does for PDF export. For example, as a first approximation, this will allow you to get the dates in the HTML output, although they are not nicely formatted - but it's a beginning:
#+MACRO: date @@latex: \hfill\normalfont{\small $1} @@ @@...
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As @rpluim mentions in a comment, setting org-export-with-sub-superscripts to nil would disable the special handling of ^ and _ for subscripts and superscripts. There is one more variable that is relevant (when org-export-with-sub-superscripts is t) and that is org-use-sub-superscripts which can be set to t or nil - or it can be set to the value {}.
I find ...
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For HTML, you can add CSS to hide borders completely. By default, I get a border width of 2 and a rules setting of group. You can override these like this:
* foo
#+ATTR_HTML: :border 0 :rules none
| a | b |
|---+---|
| 1 | 2 |
| 3 | 4 |
For LaTeX/PDF, by default I get just an \hline corresponding to the hline that I have in the table separating the header ...
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In order to use #+LATEX_CLASS: homework you must have added an entry to the variable org-latex-classes - otherwise you would have gotten an Unknown LaTeX class 'homework' error. Presumably you have already done this since you don't get that error.
To add things to the LaTeX preamble (the part before \begin{document} you need to use #+LATEX_HEADER. E.g. to ...
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