Thanks Harald for mentioning MathQuill at idea page, it saved me a lot of 
time.
So possible implementation of (3) will be:
1 - Revert MathQuill-ified text back to latex text using "
$('.mathquill-embedded-latex').mathquill('revert');"
   This will convert :
   

<https://lh4.googleusercontent.com/-kucQWjbIbOw/VQxDZjfFOuI/AAAAAAAAAVs/zZ14gedx6Do/s1600/Untitled.png>
   Into : 

   "\frac{d}{dx}\sqrt{x} = \frac{d}{dx}x^{\frac{1}{2}} = 
\frac{1}{2}x^{-\frac{1}{2}} = \frac{1}{2\sqrt{x}}"

2 - Parse the returned string to convert each Latex symbol/function to 
corresponding Sage symbol/function:
   So "\frac{x}{y}" will be converted into "(x/y)" and "\sqrt{x}" will be 
converted to "sqrt(x)"

As mentioned by Harald converting from latex to sage will take most effort 
because most probably we have to write the parser from scratch.
I will also try to contact with Desmos <https://twitter.com/desmos>and see 
if can get some help/guidance from there.

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