If you would like to check the integrity of your Juicebox-Pro zip file (to make sure that the file you have downloaded is not corrupt or incomplete), then you can check its MD5 or SHA1 hash using a free program such as HashCalc.
The 'juicebox_pro_1.4.3.zip' file should have the following MD5 and SHA1 hashes:
MD5: e6f229bca8f874217d9bee1a29cddd29
SHA1: 1ef543d1d8abd6eaa1b32395fd7ce5e35321a66d

If your own downloaded file's hashes do not match those above, then your zip file is corrupt and you will need to download the file again.
If you are having trouble downloading the file, then please try using a different browser (Chrome, Firefox, IE, Opera, Safari), ensure that you have JavaScript enabled before clicking the download link and temporarily disable any download accelerators or managers that you may have installed.

If your own downloaded file's hashes do match those above, then your zip file is fine and you should be able to unzip it and install JuiceboxBuilder-Pro and the Lightroom plugin following the instructions on the following pages:
JuiceboxBuilder-Pro: http://www.juicebox.net/support/juiceboxbuilder/
Lightroom plugin: http://www.juicebox.net/support/lightroom/

From the look of your first screenshot, it looks like you unzipping program (WinAce) is trying to extract the 'JuiceboxBuilder-Pro.air' file when you double-click it. This could be due to an incorrect file association on your computer.
.air files should be associated with the Adobe AIR Installer rather than WinACE. You should be able to unassociate .air files from running with WinAce within WinAce's options. This should revert to the default file association program for .air files.
Otherwise, uninstalling and reinstalling Adobe AIR should reinstate the correct file association.

Alternatively, as long as Adobe AIR is installed, the following should work fine to install JuiceboxBuilder-Pro (even if the file associations are incorrect or missing):

• Right-click the 'JuiceboxBuilder-Pro.air' file.

• Select 'Open with -> Choose default program...'.

• Click the 'Browse...' button in the pop-up window.

• Navigate to the following file and select (highlight) it: C:\Program Files (x86)\Common Files\Adobe AIR\Versions\1.0\Adobe AIR Application Installer.exe

• Click then 'Open' button.

You may need to show hidden files to navigate to this location: http://windows.microsoft.com/en-us/wind … dden-files

With regard to installing the Lightroom plugin, you should not be clicking directly on the 'galleryInfo.Irweb' file.
Just follow the installation instructions on the plugin's support page (link above).
Essentially, just copy the entire 'juicebox_pro_1.4.3/adobe-lightroom-plugin/juicebox_pro.lrwebengine' folder (not just the contents) to your Lightroom 'Web Galleries' folder ('C:\Users\username\AppData\Roaming\Adobe\Lightroom\Web Galleries\'). 'Juicebox-Pro' should then be listed as a Layout Style in the Web module.

Hopefully the information above will help.