In principle, you can have folders in the root file system (
/) for data without affecting or damaging system operation (apart from the fact that you risk damaging the file system if you commit an error while attempting to create folders). However, it is not elegant practice.
There is an agreed-upon file hierarchy standard in linux.
/mnt traditionally is just a quick mount point for a temporary file system.
/media is where removable media are mounted. Except for
/home, all other folders essentially host system files. How
/home is implemented is, however, not defined by this agreement. So that would lead me to conclude that any user data that is not on separate partitions belongs somewhere under
User data in first instance resides under the user's home folder, which commonly is
/home/<userlogin>. Thus, if you are the only user of that system, store "Videos", "Doc" etc under your home folder, preferably even in the folders that in an Ubuntu install are foreseen for that purpose.
If there is data you want to share with multiple users, I would recommend creating a folder
/home/data, and then put your folders "Videos", "Doc" etc there. You can use symbolic links to create very convenient access to these folders for each user that needs it. Symbolic links act and feel like real folders, and allow you to create a folder in the home directory of the user that seamlessly brings the user to another part of the file system hierarchy. Of course, you may need to adjust permissions and groups of these folders to grant the users .
With respect to "Applications", stick to the maximum extent to software provided through the APT software management system of the distribution, or alternatively, to software from snap (available by default in Ubuntu), or flatpak or appimage. Other ways to get software may incur a risk to break the system, entail technical knowledge, or increase the risk to be exposed to malware.