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1.
That is. How could I introduce diagrams in my question (written originally in lyx/latex)?

Thx.
2.

MathJax doesn't (yet) have support for any diagram package (like xypic or tikz).

If you're talking about a picture diagram, I think the easiest thing to do is to take a screenshot, upload the image to some free image hosting site and include a link (as I did in this question).

If you're talking about a commutative diagram, I usually make the diagram in an array (as in this question). If you need to draw a more complicated commutative diagram with bending arrows and other fanciness, it's probably easiest to resort to the screenshot method.

3.

Are there any plans to ever include support for a diagram package in MathJax? It seems extremely difficult without server side rendering. Perhaps one day we could have an "extended math mode" on MO that did the rendering server side.

4.

When we contacted the MathJax folk (just over a year ago), it sounded like implementing some subset of xypic was in the long-term plan. I don't know of any concrete plans yet, but I'm not especially in the know. There are certainly bigger fish to fry first, like implementing a cache.

5.

This is not strictly on topic. I just learned about JSXGraph, a javascript diagram library. The examples look fantastic, and it looks like it's extremely easy to make them interactive (I think they might actually be interactive by default). This is off-topic for two reasons:

1. You have to write the diagrams in javascript. I don't think there's a way to automatically convert your tikz or pstricks diagrams.
2. You can't use it on MO. Script tags are stripped when you post on MO (or any other forum) because allowing random users to include javascript is a huge security risk. If you have a blog, you should be able to include JSXGraph diagrams.
6.

... or you could automatically convert your TikZ diagram to SVG and include it as it is with no javascript trickery. (Does MO support SVG? Somehow, I doubt it; so that remark is for bloggers as well.)