If I can sum your post, it looks like your going into the realm of game modding. The game engine is the backbone and is restricted from players but the game logic will be barebones but customisable.
If you really want people to use their own language like C, Lua, Python, the game engine will need a bridge interface for said language for the engine which exposes the accessors of the game logic so you can override them.
I'm not sure if I understand code compile checking. Some languages like Lua, Python are interpreters and require a runtime to execute scripts and checks errors as it executes, they are also easier to incorporate into game which is why its popular for game modding. C like languages will have to compile first and upon success it will create a static code which can then be loaded into the game's memory. Think of C's output are plugins that produce dlls or .so object files when the game is run. Lua, Python, Ruby will execute the code directly by interpretation.
This is going to be a huge project, what languages are you planning to incorporate?
Interesting that you mentioned spaceships, autopilots, I just heard recently that Notch aka Minecraft creator is working on a MMO space game which includes an in-game 16-bit CPU virtual machine that will run assembly code customised to affect how your spaceship will run.
Pretty much what you described, but everything is done at low-level. Someone said that its possible to program a rocket injected with a virus and if anyone doesn't have their shields protected with anti-virus, it can your ship's system down or perhaps change it of-course to a nearby blackhole(game over=rewrite code from scratch). The daunting part for most players is that it will be coded in assembly, but he said that players have the right to exchange code within the game to build economy in exchange of currency. I can see that geekiest programmers will be ranked the richest.