I need to perform a factory reset on my computer, but, I want to keep my Unity projects and code. I am worried though that if I just copy the file there will be compatibility issues with the new editor. SO is it okay for me to just copy the file onto a USB drive and then just copy it into the projects folder of my new Unity Editor? Will there be compatibility issues with settings in the new editor? If possible is there a way to copy my entire Unity IDE and projects (everything in the Unity program)?
Just copying out the complete project folders and using an updated version on Unity should be absolutely fine 
You won’t be able to copy the Unity program and run it on a different machine, it needs to be installed and registered.
Obviously you should make backups of the projects, and if you’d rather not upgrade Unity after your reset you can always get older versions from Unity’s download archive.
Nope doesnt work on OSX. I have copied whole directory trees, Zipped them, etc and many times (but not always), the next time I try to open the project, all the scenes are disconnected from assets, etc. Unity 5.4.3f1 Personal