Make sure you select CUBASE AI... not LE, not Elements, but AI.

Start with this basic Setup Guide:
Montage and Cubase Setup Guide

If get stuck or have specific questions post back here and provide your computer Type and Operating System.

I downloaded Cubase again, this time the 32 bits version. Started on page:
http://www.steinberg.net/en/landing_pages/cubase_ai_8/download.html

I have an account already, so I downloaded this file:
Cubase_AI_8_Installer_win

after unzipping it contains a file "Cubase AI 8" which contains "start center" and the map "Cubase LE AI Elements 8 for Windows"
start center installs LE and not AI8

My operating system is Windows 10 Home, version 1511
My laptop is an Acer Aspire - i7 4510 - 8,00 GB - 64 bts

Drop a quick email through your MySteinberg Account; they will get you straightened out on opening Cubase AI8 from that install.

Steinberg sends me the same links as I've had before

Cubase AI 8.0
http://www.steinberg.net/index.php?id=downloads_cubase_ai_8&L=1

This installs the versions I already have.

For the driver, they refer to manufacturer's website. I downloaded a newer version V1.9.9

Unfortunaly Cubase can't load the audio driver

I sent Steinberg another email, hope it can be solved in order to do some recording.

Unfortunaly Cubase can't load the audio driver

Not sure, but since this sentence is not at all clear... Let's go over what is supposed to happen. The Steinberg program that you downloaded and presumably activated (correct?) is Cubase LE AI ELEMENTS... When you launch it please select CUBASE AI, not LE, not Elements... "AI8"

Install the driver, Yamaha Steinberg USB for Windows v1.9.9, to your computer (Cubase should be closed during this installation, the driver is installed and loaded on your computer) then when you launch Cubase it will find the driver.

Let's verify the driver installation:
On your Windows 10 computer navigate to your CONTROL PANEL
Find "Hardware and Sounds"
In here you should see a red icon for "Yamaha Steinberg USB"
Click that to open its info.
Verify that you have version 1.9.9

Let us know.

I didn't bother downloading Cubase AI as I already had a copy of Cubase Elements - is there any advantage to AI over Elements? Plus I'm not sure if I have still have the code that came with my montage.

@ Phil
I believe the licensed version of Elements includes the same extras as AI...as far as Montage is concerned. For a complete listing of differences you'll want to query Steinberg via your MySteinberg Account.