I can delete files from a client machine without issue. I do it all the time.
One thing that is annoying is that sometimes when you delete a file from the client, the server pops up the "Do you want to remove this now-empty folder?" dialog, which stinks. But if it really annoys you, you can just tell it not to ask you anymore.
I don't think renaming files on disk (via Rename, Move, and Copy or whatever) actually works, but I haven't tried it in a long time.

Changing the [Name] tag, though, works fine, as does changing any other tag.