My school offers the adobe-programs on the school-owned computers. To be able to use those you do however need to log into you adobe-account evertyime you open any adobe program on these computers, although you simply need a log-in an can access the adobe programs even without having a subscription of your own. I would like to buy the adobe-package to be able to use the programs on my personal computer, which I then would be using the same adobe-account for as on the school computers. Would buying the package with my already existing adobe-account, meaning using the same log-in for the school computers as for my own, cause a problem? Is the fact that I currently for free can log in on with my adobe-account and use the programs on the school-owned computer something that could be disturbed by me buying my own subsciption with the same log-in? I also have some images saved on the Creative Cloud that I wouldn't want to be lost. I would also like to be able to use the adobe-package on my own two devices, still being able to log in to the school computers without that computer being seen as one of these devices and yet being able to acccess the same creative cloud.
Gladly take any advice on wether this seems possible or not!
Just don't.Using the same email address will get you a world of pain. If it's a school email you will lose both of the accounts at the same time. And if it's not a school email, choosing between the two (identical) accounts may be difficult. There's also every chance that you will end up paying on the wrong account. You would NOT magically share Creative Cloud files by using the same email.
You should also make sure you have backups of everything on Creative Cloud. It could disappear any time due to technical problems, mistakes, or decisions by the school. It would NOT be shared with the new account, so do it from the old.
It's not rock science, and I would get it running using my school's ID, but only because I'm an experienced user and know when it's working and when not, and how to work around the limitations.
It looks like your school uses licences locked to the computer and not to your Adobe ID. If it were locked to your Adobe ID, you would be able to use the same ID on your computer. You can take a Creative Cloud subscription, but as @Test Screen Name says, use a different ID. Do not use your school's e-mail, if that is connected to your school Adobe ID. You may use that, however, as a rescue e-mail as long as you are a student. You will get the student price also with a non-school e-mail.
For sharing data, you can always share via the cloud, but initiate the share from your private account. And it's always a good idea to keep a backup of your cloud data (this is true for any cloud service). Even if the cloud service is backed-up by the service provider, you are never better served than by yourself.