You can easily do those things in DW. Move, copy, paste, duplicate, delete, rename. You can accomplish things using shortcut menus or keys, or drag and drop. When you rename/move files, DW will ask you if you want to update links. It also has a synchronization function that will show you files changed locally, remotely, or both.

You can try DW yourself for 30 days for free to make sure. I had DW MX before and wasn't sure about upgrading to MX 2004, but it is worth it to me now because I use CSS. Otherwise, I don't see much difference between the two versions.

It's hard to show... so I'll give you a link to a DW tutorial: http://macromedia.breezecentral.com/r61914037/
It was very helpful.

Basically, with MX, I had to go through the stylesheet to look for settings I wanted to change. In 2004, there are panels that show the styles, the setting, and possible settings, so I don't have to constantly look them up. I didn't deal with CSS in MX so I don't know what its capabilities are, but the person who gave the tutorial made references to them.