Variable type change

If the "from" you've shown works (or worked when you were using jQuery), canvas2 is or was a jQuery object (most likely). The rough equivalent is your first line, but on the DOM element inside it:

canvas2[0].addEventListener('mousedown',function(e){handleMouseMove(e);}); 

or indeed, simply:

canvas2[0].addEventListener('mousedown', handleMouseMove);

Naturally, if you're trying to migrate code away from jQuery, you'll probably end up changing canvas2 to something else, perhaps a straight DOM object. If so, drop the [0] from the above when you do that. But as the first line of the things you've tried would have worked if that were already done, hopefully the above helps.

Side note: You changed from handleMouseDown to handleMouseMove in your examples. I've faithfully done that above, but do be sure you're using mousedown with handleMouseDown and mousemove with handleMouseMove...