Is it problem free to delete Cubase 12 and 13 when using Cubase 14?
No, you can use the different versions independently of each other or in parallel if you like. Removing a version doesn’t affect the other ones. Maybe you might want to keep Cubase 13 for the time being until Cubase 14 gets some stability fixes.
Not a problem at all, but sometimes it’s a good idea to hold on to the previous versions for a while. The newer one does not take up much space
edit: @Martin90 posted while I was typing
I was thinking maybe the plugins would be deleted as well?
Yes, the bundled plug-ins which are installed together with the Cubase application (and not by separate installers) are deleted too because they are located in the corresponding Cubase program folder. But since they are tied to that Cubase version and are reinstalled with the new versions as well, this shouldn’t matter.
Keep the installers.
Assuming they have their own installers, these are separate from Cubase.