I notice that you have the embedding code correctly inserted into your http://www.hotelmandarina.com/rooms_rates.html page.
However, the path to the 'juicebox.js' file within the embedding code is incorrect.
Copy the contents of your gallery folder to the root of your web space (alongside the 'rooms_rates.html' file) and your gallery should display fine.

Your gallery (the 'juicebox-container' <div>) is horizontally centered within its parent container and, within the gallery, the thumbnails are centered within the thumbnail area and the main image is centered within the image area. Most of your main images are portrait style and, in a landscape style gallery, there is space to the left and right of the main image. Try resizing your gallery browser (by reducing its width) and you will see that the thumbnails and main images become closer together.

This is because you have set thumbsPosition="LEFT" and thumbNavPosition="BOTTOM".

Currently, there is no configuration option available to horizontally align the main images to the right edge of the image area. However, in a browser window of a certain aspect ratio (closer to portrait than landscape), the right side of your main images will be flush against the right edge of the gallery. Try resizing your browser window and you should see this.

My suggestions above would move the thumbnails away from the left edge of the gallery.
If you wanted the thumbnails as close to the main images as possible (for images of all aspect ratios), you could set the following configuration options:

thumbsPosition="LEFT"
maxThumbRows="3"
maxThumbColumns="3"
thumbNavPosition="BOTTOM"
thumbPadding="0"
imagePadding="0"
imageScaleMode="FILL"

Changing thumbNavPosition from "BOTTOM" to "CENTER" will reserve space to the left and right of the thumbnails for the thumbnail navigation arrows.
As I noted above, there are currently no configuration options to horizontally and vertically align the thumbnails and main images within their respective areas but such options should be introduced in the next version of Juicebox-Pro.

It sounds like you have entered the embedding code as plain text rather than as HTML code. Make sure that the method of entry is correct (use Code View).

This is simply the name of the HTML page created by JuiceboxBuilder-Lite in order to display the gallery on a page of its own (for example, when previewing the gallery immediately after creation). If you plan to embed the gallery in an existing web page alongside other content, this HTML page is not actually required so it does not matter what you name the file.

You have a stray double-quote in your code.
Change:

<div id="juicebox-container" "style="margin: 0 auto;">

... to:

<div id="juicebox-container" style="margin: 0 auto;">

However, your gallery is horizontally centered within its parent container.

If you wish to increase the distance between the thumbnails and the left edge of the gallery, you could:
(1) Change thumbNavPosition="BOTTOM" to thumbNavPosition="CENTER"
(2) Increase the value of the thumbPadding configuration option
(3) Increase the value of the stagePaddingconfiguration option

The next version of Juicebox-Pro will also introduce configuration options which will allow you to horizontally and vertically align the thumbnails and main images within their respective areas (although I do not know when it will be released).

I think I may have discovered the reason for your problem.
In your galleries, the paths within your embedding code use the www subdomain of finecustombuilding.com (www.finecustombuilding.com) and your galleries will display fine if visiting www.finecustombuilding.com.
However, all gallery files must be located on the same domain (or subdomain) as the web page into which the gallery is embedded (due to the JavaScript same origin policy) and your gallery will fail if you access your page via finecustombuilding.com rather than www.finecustombuilding.com.

Either ensure that your clients visit www.finecustombuilding.com or use relative paths within your embedding code so that your galleries can be viewed at both www.finecustombuilding.com and finecustombuilding.com.

For example, in your 'projects.html' file, use the following embedding code:

<script src="jbox_gallery3/jbcore/juicebox.js"></script>
<script>
  new juicebox({
    baseUrl : 'jbox_gallery3/',
    containerId : 'juicebox-container3',
    galleryWidth : '930px',
    galleryHeight : '700px',
    backgroundColor: '#222222'
  });
  </script>

A Juicebox gallery should work fine in a page using an XHTML Doctype Declaration.

Make sure that you are using the current version of Juicebox-Lite (v1.2.0).
If necessary, instructions for 'Upgrading Juicebox' can be found here.

Also, try re-uploading your gallery's 'jbcore' folder to ensure that all necessary files are present and correct in case something happened to corrupt the 'juicebox.js' file on the initial upload.

If you continue to experience difficulties, please post the URL to your web page so that I can take a look.

@graphitegolem

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Just try opening Adobe Extension Manager first and then go to 'File -> Install Extension' from the drop-down menu at the top (and navigate towards the .mxp file).
I have fixed the link in my previous post. (The instructions for installing the CS2/CS3 version are on the Photoshop Template page.)

Rather than double-clicking the .mxp file, try right-clicking the shortcut for Adobe Extension Manager, selecting 'Run as administrator...' and then go to 'File -> Install Extension' from the drop-down menu at the top (and navigate towards the .mxp file).
Otherwise, download the Photoshop Template for CS2 or CS3 and following the installation instructions here.
Once installed, the plugin files for CS2/CS3 are identical to those for CS4 or higher, only the method of packing the files (.zip vs .mxp) differs.

Instructions for 'Embedding in a Web Template Site' (which should work for your scenario) can be found here.
It sounds like you may have been following these instructions but it is difficult to know exactly what is wrong without seeing your web page.

You should be able to see your gallery by opening the public link to the gallery's 'index.html' file directly in a browser.
If you do not see your gallery, then the link may not be a public link or all your gallery files may not be uploaded to your Dropbox account.
If you can see your gallery, then there may be a problem with the iframe code on your embedding web page.
If you continue to experience difficulties, please post the URL to your gallery so that I can take a look and help further.

Yes. Set changeImageOnHover="TRUE" in your gallery's XML file.
If using JuiceboxBuilder to create or edit your gallery, this configuration option can be found in the 'Customize -> Main Image' section.
For reference, a complete list of all configuration options can be found here.

Increase the imageTransitionTime from 0 to something like 0.1 and your first image should initially be visible.

The next version of Juicebox-Pro should hopefully introduce the ability to vertically and horizontally align the main images and thumbnails (although I do not know when this will be released).

stagePadding and imagePadding configuration options should work fine.
If you have a gallery in which the stagePadding or imagePadding does not work as expected, please post the URL so that I can investigate further.

Please see the Known Issues section of the JuiceboxBuilder User Guide. (This is due to limitations within the Adobe AIR web browser.)