I am reading this book why does $E=mc^2$ and I learned that causality is what proves that there is a cozmic speed limit-I'm the only one here who is astonished by the looks of it ;-). Anyway. Would a 100% random machine break the law of causality. To visualise it- Think of the universe as a film. In the middle of the film a random event occurs that changes the future of the film. If you rewind it back to the randomised bit something different may occur or by chance the same thing would happen again.
You seems to be mixing up to different notions of causality.
Consider the two principles:
- Every cause must precede it's effect
- Every event must have a cause
The rule against superluminal motion in special relativity is intended to insure (1), but doesn't care about (2).
In the rest of your post you seem to be talking about (2). That second statement has a long history in philosophical circles but things like Norton's Dome leave it is a bit of a gray area even in pure classical mechanics.
Yes, real randomness is a concept that breaks causality. It is not agreed upon that any such thing exists.
But note that it suffices for most human purpose that a process has obscure or inaccessible causes, in order to be considered random. Where necessary, this latter concept is referred to as "pseudorandom".
I wouldn't say that causality necessarily proves that a "speed limit" exists, although as attributed (probably apocryphally) to Einstein, "time is what stops everything happening at once" - that is, at least some set of natural processes must be non-instantaneous, in order to prevent immediate universal oblivion.
But there is not, a priori, any requirement for every process to be non-instantaneous.