Yes, you can do this. You can reference an external DLL from the RightEdge project and call into it as necessary.
You can put logic that applies across all symbols in the MySystem class. One instance of this class is created for your system, while MySymbolScript is created once per symbol.
For your system to trade a symbol, it needs to be in the watch list and selected when you run the system. So you will need to have all the symbols you may want to trade in the watch list when you run the system.
This should point you in the right direction, let us know if you run into any trouble.