Secondly, in the typical Smalltalk implementation, there is still compilation, but it's incremental. You compile expressions and methods, not the whole body of source code for the whole system. What's really different about it is since the semantic actions are late-bound, you can even compile something while a thread is executing through the code you're compiling. So, you get nearly instant feedback on changes for free. Bret Victor's notion of programming environments blurs the axes you're talking about even more, so that you don't have to do two steps to see your change, while a thread is running (edit, then compile). You can see the effect of the change the moment you change an element, such as the upper bound of an iterative loop. To make it even more dynamic, he tied GUI elements (sliders) to such things as the loop parameters, so that you don't have to laboriously type the values to try them out. You can just change the slider, and see the effects of the change in a loop's range very quickly, such that it almost feels like you're using a tool-based design space, rather than programming.
I don't know how this was done in ST-78, but in ST-80, at least in accounts I've heard from people who've used versions of it, and in the version of Squeak I've used from time to time, the source code is not technically stored with the class object, though the system keeps references to the appropriate pieces of source code, and their revisions, mapping them to the classes in the system, so that when you tell the system you want to look at the source code for a class, it pulls up the appropriate version of the code in an editor.
Source code is stored in a separate file, and Smalltalk has a version control system that allows reviewing of source code edits, and reversion of changes (undo). The class object typically exists in the Smalltalk image as compiled code.
There are many things that are different about this vs. what you typically practice in CS, but addressing your point about data, in OOP, objects are supposed to take the place of data. In OOP, data contains its own semantics. It inverts the typical notion of procedures acting on data. Instead, data contains procedures. It's an active "live" part of the programming that you do. So, yes, data is persisted, along with its procedures.
A simple example in Smalltalk is: 2 + 2. If we analyze what's going on, the "2"'s are the pieces of data, the objects/servers, and "+" is used to reference a method in one of the data instances, but it doesn't stop there. The "2" objects communicate with each other to do the addition, getting the result: 4. As you can tell implicitly, "2 + 2" is also source code, to generate the semantic actions that generate the result.