Unfortunately you have asked 3 questions, it is tricky to address them all at once.
I will explain how to position DIV element on top of some 3D object. My example would be a tooltip that appears when you hover the object by mouse: http://jsfiddle.net/mmalex/ycnh0wze/

So let's get started,
First of all you need to subscribe mouse events and convert 2D coordinates of a mouse to relative coordinates on the viewport. Very well explained you will find it here: Get mouse clicked point's 3D coordinate in three.js
Having 2D coordinates, raycast the object. These steps are quite trivial, but for completeness I provide the code chunk.
var raycaster = new THREE.Raycaster();
function handleManipulationUpdate() {
// cleanup previous results, mouse moved and they're obsolete now
latestMouseIntersection = undefined;
hoveredObj = undefined;
raycaster.setFromCamera(mouse, camera);
{
var intersects = raycaster.intersectObjects(tooltipEnabledObjects);
if (intersects.length > 0) {
// keep point in 3D for next steps
latestMouseIntersection = intersects[0].point;
// remember what object was hovered, as we will need to extract tooltip text from it
hoveredObj = intersects[0].object;
}
}
... // do anything else
//with some conditions it may show or hide tooltip
showTooltip();
}
// Following two functions will convert mouse coordinates
// from screen to three.js system (where [0,0] is in the middle of the screen)
function updateMouseCoords(event, coordsObj) {
coordsObj.x = ((event.clientX - renderer.domElement.offsetLeft + 0.5) / window.innerWidth) * 2 - 1;
coordsObj.y = -((event.clientY - renderer.domElement.offsetTop + 0.5) / window.innerHeight) * 2 + 1;
}
function onMouseMove(event) {
updateMouseCoords(event, mouse);
handleManipulationUpdate();
}
window.addEventListener('mousemove', onMouseMove, false);
And finally see the most important part, DIV element placement. To understand the code it is essential to get convenient with Vector3.project method.
The sequence of calculations is as follows:
- Get 2D mouse coordinates,
- Raycast object and remember 3D coordinate of intersection (if any),
- Project 3D coordinate back into 2D (this step may seem redundant here, but what if you want to trigger object tooltip programmatically? You won't have mouse coordinates)
- Mess around to place DIV centered above 2D point, with nice margin.
// This will move tooltip to the current mouse position and show it by timer.
function showTooltip() {
var divElement = $("#tooltip");
//element found and mouse hovers some object?
if (divElement && latestMouseIntersection) {
//hide until tooltip is ready (prevents some visual artifacts)
divElement.css({
display: "block",
opacity: 0.0
});
//!!! === IMPORTANT ===
// DIV element is positioned here
var canvasHalfWidth = renderer.domElement.offsetWidth / 2;
var canvasHalfHeight = renderer.domElement.offsetHeight / 2;
var tooltipPosition = latestMouseProjection.clone().project(camera);
tooltipPosition.x = (tooltipPosition.x * canvasHalfWidth) + canvasHalfWidth + renderer.domElement.offsetLeft;
tooltipPosition.y = -(tooltipPosition.y * canvasHalfHeight) + canvasHalfHeight + renderer.domElement.offsetTop;
var tootipWidth = divElement[0].offsetWidth;
var tootipHeight = divElement[0].offsetHeight;
divElement.css({
left: `${tooltipPosition.x - tootipWidth/2}px`,
top: `${tooltipPosition.y - tootipHeight - 5}px`
});
//get text from hovered object (we store it in .userData)
divElement.text(hoveredObj.userData.tooltipText);
divElement.css({
opacity: 1.0
});
}
}