Lot of the things that are on your list are already implemented:
tex4ht can produce xhtml with mathmltex4ht can produce SVG figures from tikz/pgf figures- METAPOST already outputs SVG out of the box
- Linking to parts of your documents is done by the
hyperref package, for pdf and html/xhtml.
Connecting to Wolfram|Alpha is surely not a "web standard", and may be difficult, since math in TeX is mostly described in a "presentation", rather than semantic way. On the other hand, it should be possible to do it for each individual equation using the hyperref package. I do not really see any way to do it automatically.
I know it is possible to produce tooltips and include animations in a pdf document, I am not sure how would that work when converting to html.
Update 07/2020:
The code bellow is not needed anymore. TeX4ht has now full support for the MathJax output. The equivalent of the code bellow is this:
make4ht filename.tex "mathml,mathjax"
If you want to keep your LaTeX math as plain text, use just:
make4ht filename.tex "mathjax"
make4ht is replacement for htlatex that converts to HTML5 and UTF-8 by default, so no special configurations as in the old answer are necessary.
Original answer:
You can use TeX4ht. It can output math as mathml which can be then displayed with mathjax. You can also configure html header to load mathjax script from mathjax's cdn:
\Preamble{xhtml,mathml}
\Configure{VERSION}{}
\Configure{DOCTYPE}{\HCode{<!DOCTYPE html>\Hnewline}}
\Configure{HTML}{\HCode{<html>\Hnewline}}{\HCode{\Hnewline</html>}}
\Configure{@HEAD}{}
\Configure{@HEAD}{\HCode{<meta charset="UTF-8" />\Hnewline}}
\Configure{@HEAD}{\HCode{<meta name="generator" content="TeX4ht
(http://www.cse.ohio-state.edu/\string~gurari/TeX4ht/)" />\Hnewline}}
\Configure{@HEAD}{\HCode{<link
rel="stylesheet" type="text/css"
href="\expandafter\csname aa:CssFile\endcsname" />\Hnewline}}
\Configure{@HEAD}{\HCode{<script type="text/javascript"\Hnewline
src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"\Hnewline
></script>\Hnewline}}
\Configure{@HEAD}{\HCode{<style type="text/css">\Hnewline
.MathJax_MathML {text-indent: 0;}\Hnewline
</style>\Hnewline}}
\begin{document}
\EndPreamble
With this config file, we request to output math as mathml, then configure html header so resulting file is html5. Save it as for example ht5mjlatex.cfg and then call from command line:
htlatex filename.tex "ht5mjlatex.cfg, charset=utf-8" " -cunihtf -utf8"
or you can use William F. Hammond's script (at bottom of the page)
Best Answer
Although it doesn't convert LaTeX directly into HTML, I can really recommend PDF2htmlEX. It's a free software project, which delivers stunning results from the output of PDFtex. Its available for all major platforms (Linux, Mac Windows).