Hello.
I have a few questions:

1) Could this system be used or modified to be used as part of the joomla CMS?
2) Does it support multi-level access? i.e. if the user gets over 60% in the test they will be presented with another test that they can take
3) Could there be multiple users taking different tests all at once

Ideally the individual user would need to follow this process:

a)They would login to a members area of our Joomla website (already developed),
b) They would take a test
C) The results of the test (automatically retrieved by the database) would tell the user what their skill level was.
D) Dependent on their skill level another test would be provided for them to take
E) After each test, their score would be presented and a further test will be presented to them.

Thankyou for your time

1. There has been a Joomla extension called "joosurvey" but this is completely outdated and not maintained anymore.
You can run Limesurvey within an iFrame of a joomla system I guess but you might need to code some scripts to use the same user information. More information:
1.1 Search the forum for "joomla".
1.2 Maybe you can use the one-time-password feature to login joomla users to the admin backend: docs.limesurvey.org/tiki-index.php?page=...e_one_time_passwords
1.3 Check the CMS integration settings:
"// CMS Integration Settings
// Set $embedded to true and specify the header and footer functions - for example if the survey is to be displayed embedded in a CMS
$embedded = false;
$embedded_inc = ''; // path to a php file to include
$embedded_headerfunc = ''; // e.g. COM_siteHeader for geeklog
$embedded_footerfunc = ''; // e.g. COM_siteFooter for geeklog"

2. You can forward the user to a script which has to be coded and calcultes the score at the end of the survey and redirect them automatically to another survey.

3. You can run X surveys with Y users at the same time.

a-e) This can partly be done with some additional coding.

Sad to see that you are not interested in integrating Joomla with Limesurvey...

after all you ARE using Joomla! to host this website...why not integrate the two? You would be the best survey component for Joomla! by a longshot...

You can't say we are not interested. If there is a user asking for help to integrate Limesurvey into joomla we'll definately try to help.
Fact is that no one of our team mebers has enough free time to take care of this. But if you want to give it a try you are welcome.