You also underestimate the difficulty of turning an idea into a product. Writing code to build an app or a website is only the first step, getting engaged users and growing is far more difficult.
> By now they have all the resources and flexibility (hundreds of engineers only busy at exploring ideas)
FB employees are certainly not "only busy exploring ideas", I don't know where you got that idea from.
In case FB were to do this, it would attract the US Government's attention for monopolistic practices.
As opposed to "stealing" your idea, FB (and other large companies) would be more interested in aqui-hiring a successful startup.
So yeah, you certainly don't need to be worried about FB stealing your idea.
Not convinced yet? Look at the startup ecosystem, how often do you come across one of the large companies stealing a startup's idea? I can't think of many.