As a general case, you would need a backup that's either a system copy or a Time Machine backup to restore anything (apps, settings, passwords, certificates, user accounts, and such) to a machine.
Depending on how the company has installed the applications, they might be tied to an App Store model and things that are signed applications won't run without the password or a valid enterprise entitlement/MDM pushing updates to the applications.
It would be hard to guess what happens if you tried to restore that backup or if you tried to manually reinstall some things (say you wanted the documents you personally were responsible and allowed to recover).
In an ideal world, you would get some IT help to thin the things that need to be removed from the device and get their blessing to make a backup of the things you can realistically restore.
Then you would need to purchase licenses for the software or seek alternative apps that are priced in a way you wish to spend to make your personal computer get things done you need. Not everyone needs photoshop, for example. Things like Acorn or Pixelmator do a fantastic job at a different price point than Adobe's product.
Lastly, don't overlook how many documents Apple's core notes, Preview, iCloud web apps can edit and annotate quite well.