install rsync

It's probably already installed. Have you checked your package list in the WebIF? If it's not installed you can install it from there at the touch of a button.
sohlinux:What is the command to install rsync?
If you must do it from the command line, (It's better to use the Web-If installer if available) enter :-
opkg install rsync
It depends on dropbear-ssh being present
No :) I do have some rsync servers.

I'm also likely to use it to mirror two local directory structures such as one disk to another.

I agree, the dependency on dropbear should be removed from the package.

Posted on the move. Please excuse any brevity.