Is there a way to put the iPhone into a child-only mode? I find that my two-year-old will often delete photos...most of the times by accident.

Is there a mode on the iPhone or some other software that will help thwart this?

Is there a way to control which apps a child can access?

(I'm hoping that Apple would build it right into the OS.)
Yes, start with Guided Access which easily locks one app in full screen mode and then move on to restrictions once you have a feeling for what you want to open up past one app at a time as your two year old gets more able to use more than just one game at a time..