NTFS, fat32, exfat, could I theoretically create my own filesystem?

Yes. There are many different file systems and with a bit of work you can absolutely create your own. Making one that is reliable and performs well, and/or is something you can actually use for the disk that you boot from, is a lot of work and generally involves low-level kernel programming - not exactly a beginner’s programming project.

However, you can also more easily play with implementing filesystems in a high-level language using FUSE.

If so would my computer even be able to work with most files or connect to other devices?

Your computer can use many different filesystems at the same time. You can also store a filesystem in a file on another filesystem, rather than dedicating a partition of a physical disk to it. So, yes, you can use a filesystem of your own design at the same time you are using other storage devices formatted with more common filesystems.