I am not sure what exactly do you mean. Shape layers in Ae are very versatile and you can stack up strokes and fills as much as you want, group them together to make a new shape but everything is layered out. there is not "Expand appearance" because Ae is a non-destructive application. perhaps you can specify exactly what your are set to accomplish and provide screenshots and we can give you a workflow suggestions.
a quick guess - if you want to be able to animate rounding corners, add a rectangle and play with the roundness
The closest thing to converting a stroke to a fill in AI would be to use "Trace" from the Layer menu in AE. However, you will not get great results most of the time, as it works similar to the Trace command in AI. Basically it results in approximate paths, generally with a lot more vertices than you want or need, and not all will follow your original shape perfectly. Your best bet would simply be to make sure you've outlined your stroke paths in AI before working with them in AE. As for dynamic edge rounding, this can only be done using the basic geometric shapes created in AE natively, not to anything made using the pen tool or bezier paths.