Better Markdown support: Built-in LaTeX, syntax highlighting, header IDs, etc

It'd be nice with built-in support for all this: (and maybe simpler to fix these things at the same time)

• CommonMark syntax inline help, see: Inline CommonMark formatting help
• Maths (LaTeX via KaTeX), and preferably disable CommonMark's handling of underscore _ and backslash \, so people won't need to write e.g. \int\_fromSomething^toSomething.   (In CommonMark, _ otherwise makes text italic:; _italics_ becomes: italics).
• Source code syntax highlighting (Prism.js) (see: How to add Syntax Highlighting). And support many languages (not just one).
• Diagrams (Mermaid)
• Auto generate heading IDs (for deep linking into a doc. See: Headers don't have IDs?)
• Checkboxes: [ ] do something
• All links to external web pages could optionally open in new tabs — make configurable?
• ~~Strikethrough~~, see: Markdown: strikethrough
• Box-shadows around <img>? See: Add a border to images

It's not so good if (like now) people need to add their own javascript tags to make the above things work. And heading IDs and checkboxes cannot be made to work, in that way, I think.