Basically, if you, as a regular user, cannot unmount a device, you can usually just go to root shell (sudo -i), see where the thing is mounted (just use mount) and then unmount it (umount /media/blah/floop). If it says the device is still busy, as root you can remount it as read-only and then unmount it (seeking documentation left as an exericise to the reader, as I'm sitting at a Windows system now).

There's also lsof ("list open files") tool, which can be used to see which exact programs are using files on that device, which you can then use to kill those sneaky processes (ps, kill).

Real answer: it depends.

• Deleting a file in use: no problemo. File is removed from the directory immediately, but exists on disk until last program who had the file open closes. Everyone wins! (Unless you're trying to free up space by deleting a huge file that's being held open by a program and not understanding why the filesystem usage didn't go down)
• Unmounting a hard drive in use: Will error out similarly to Windows. lsof can tell you which process has which files open. There's nuance with lazy unmounts and whatnot but that should not be used in most cases.

Now in practice you should be wary of one very important thing that changes compared to Windows: Writes are asynchronous on Linux. First the kernel writes to RAM, then it flushes to disk at a later time for performance reasons (this is one of the reasons why writing a bunch of small files is many times faster on Linux than Windows). The upshot is that just because your file copy is "done" doesn't mean you can just yank the USB cable. Always safely unmount before unplugging a storage device on Linux.

Linux Mint has an eject button that allows any cached writes* to finish, prevents new ones from starting, and un-mounts it. It's actually important to use the eject button as flash drives are slow, and the write cache can obscure the fact that a file isn't done writing yet.

*Copying a file will add it into the write cache while it writes out to the disk. As soon as it is in the cache, you can use the file as if it was already done copying, including making changes.

Idk how Linux handles it but today on Mac I accidentally sent a folder to trash that was in use by four programs at once.

Mac OS did not give a shit. It nuked it.

Many files copied to an external disk are cached, and not written immediately unless you run the "sync" command.

So when you press the "eject" icon, on most frontends a notification will tell you not to unplug it right away, once the write is complete it will send a "it is safe to remove the drive" message. This can take a couple minutes if you are writing a big file to a slow drive.

Linux doesn't care if you have a file open in multiple places. In fact, if you edit it in one place, it might even prompt you to overwrite with the new data, or save-as to a different file, in the other place

It generally does not care about files being read/open. If there's a write operation pending, it just shows that and then ejects.

I basically never have this problem on Linux.

I think programs can't hold removable media busy by default on Debian. If you remove, you lose whatever changes aren't there. Either way, Linux programs just read files and close them, they mostly don't keep files open.