A Microsoft file hosting and synchronization service.
1
OneDrive has a setting named 'Files on Demand', if that setting is disabled, then the users files will also remain on the PC, if that setting is enabled, then the users files are synced to the cloud, then removed from the PC to save space on the PC, then when the user wants to access a file it is downloaded so the user can edit the file, then uploaded back to the cloud.
2
You are correct, OneDrive syncs files between your devices, so you have access to your files on any device, the only way to stop that inter-device syncing, is to use a different Microsoft account on each device.
3
If you do not want to use OneDrive to sync your files to the cloud, you can unlink your account from OneDrive's settings on the PC, then uninstall the OneDrive app.