How can I make an instance of a block of Blockly with Javascript?

There is a method setWarningText to show this kind of warnings. You could modify yor generator as follows:

Blockly.JavaScript['move_right'] = function(block) {
    var value_pixels = Blockly.JavaScript.valueToCode(block, 'PIXELS', Blockly.JavaScript.ORDER_ATOMIC);
    // TODO: Assemble JavaScript into code variable.
    var codeMoveRight = "$(\"#moveDiv\").animate({\n " + 
                    "left: \"+=" + value_pixels + "px\"\n" +
                  "},1000);\n";

    // You can show a blockly warning
    if( value_pixels >= 300 ) block.setWarningText("You get it!");

    // Or you can store its value elsewere...
    // myExternalVar = value_pixels;

    return codeMoveRight;
};

This will appear as a warning icon in the block itselfs.

In any case, if you want to "remember" this value_pixels variable, I believe the more easy way is to do it in the generator, as shown above. You can always store it in an external var accessible from your custom functions.

EDIT:

If you need to traverse the block structure for some other purpose, you may use:

• Blockly.mainWorkspace.getTopBlocks(true); // To get the top-level blocks
• An iteration over the top-level block list
• block = block.nextConnection && block.nextConnection.targetBlock(); // To "descend" into the sub-blocks of a block, then iterate over them
• if(block.type=="move_right") ... // To check for a particular block type

I hope this will give a start point, but the best way to learn about these "tricks" is reading the Blockly source code. Even as the code is generally well commented, AFAIK there is no way to autogenerate a document, and it is not available on the web neither.