First, you should ALWAYS ALWAYS ALWAYS use the latest version of Firefox (23 ATM), old versions are not supported or secure. You can do one of two things in a situation such as this:

• Create a separate Firefox profile for work and school. Nothing in these profiles will be shared, so you can safely do work stuff in one profile, then switch profiles when you need to do school. Profile Manager - Create, remove or switch Firefox profiles.
• Just ignore your work. They probably want you to use different browsers so you don't get distracted as easily by non work related stuff, but if you have good self-control, just use the same profile for both.

Honestly it's up to you. I do option 2, but option 1 would work fine for you as well.

another option would be to use a portable version of firefox for your work which keeps an entirely seperate profile anyway (this is not provided by mozilla directly): http://portableapps.com/apps/internet/firefox_portable

If I create a separate profile will my apps or Firefox add ons be shared with my other profiles and if I do get the latest version of Firefox will my add on's from my previous Firefox browser be transferred to my newly updated one.

Yes, updating will bring all your data from older versions, It is stored in profiles that are kept independently of what version of Firefox you are running, so installing a new update won't change that.

You can set up Firefox sync to synchronize the two profiles, but at that point you might as well just use one profile.

I am trying to create a new profile but when I type Firefox.exe -P into the run program it opens a new window instead.

You can only open the Profile Manager if all Firefox instances are closed.

You can install multiple Firefox versions via a custom install in different installation folders and only use the older Firefox version when you really need it.
Do a custom install and install each version in its own program folder to use multiple Firefox versions.

• https://support.mozilla.com/kb/Custom+installation+of+Firefox+on+Windows
• http://releases.mozilla.org/pub/mozilla.org/firefox/releases/

See:

• http://kb.mozillazine.org/Creating_a_new_Firefox_profile_on_Windows
• http://kb.mozillazine.org/Shortcut_to_a_specific_profile
• http://kb.mozillazine.org/Using_multiple_profiles_-_Firefox

You can use the -no-remote command line switch to open another Firefox instance with its own profile and run multiple Firefox instances simultaneously.

• http://kb.mozillazine.org/Opening_a_new_instance_of_Firefox_with_another_profile