Is it possible to access the shell (Darwin) on an iPhone?

"Sure. You need to jailbreak it and install MobileTerminal (an application you'll find in Cydia for installation, once having jailbroken your iPhone).
MobileTerminal gives you access to the iPhones bash (shell).
To write decent shell scripts you would also need to install some shell utilities that you would expect to be there by default like vi, curl, openssh, ...All of this is available in Cydia as well."