Is it safe to manually delete files and folders from a time capsule? ( Apple's Time Machine backup system calls backup partitions that way )
Because using TM's option
Delete all backups of ... is taking for ever
Yes, it is safe to manually delete backups. It won't be any quicker, though. Time Machine uses hard links to save space. A hard link is where a physical file on your hard disk is mapped to by multiple logical files (i.e. what you see in the Finder). When Time Machine is backing up, it hard links all files that haven't changed. This is how it can have multiple copies of them in the backup without them taking up any space - all the logical files are pointing to the same physical files on disk.
Using hard links, however, makes deletions take a long time. When you don't have any hard links, all you need to do to delete a file is remove the logical file from your directory structure, then erase the physical file on disk*. When hard links are in use, things are more difficult because you can't just delete the physical file straight away - another logical file might be mapped to it. You need to check that none remain, and this is time-consuming. You have to do this because if you didn't, and left the physical file untouched, it'd eventually be left 'orphaned' - using up space on the disk, despite not being referenced by any logical files.
This is why the delete takes so long (actually, the "preparing to delete" period - not the actual delete itself). Deleting with the Finder wouldn't be any quicker than deleting with Time Machine - both are constrained by the underlying file system.
*It's fairly common knowledge that file systems don't normally erase the actual data on disk when a file is deleted, so if you want to be pedantic, read "erase the physical file" as "mark the physical file's locations as free".
Reformatting the drive should be the first option for most people, as manually deleting folders can take quite awhile & its pain in the rear. Also, the system may not delete files properly, and the trash does not empty completely. (Which is a minor problem)