There's a good link at AACT.org (American Association of Community Theatre) that explains the tasks and responsibilities for actors, directors, designers, etc. 

You forgot one...

I understand perfectly about stage directions, based mostly on the size and if the required stage set can be somewhat recreated per the design the author had in mind. Things need to be adjusted for the situation. But if a stage direction says 'everyone runs to the door to escape the fire about to engulf them in the restaurant' (fer' instance...) and the director says to ignore that and sit around the table and continue eating... well, that's the kind of situation I'm talking about. The 'director' changes the thing to suit their own 'vision' of what the story should be. Well, the next scene would say something like "Roy runs up to Mary who just came outside, coughing from the smoke" now if Mary is still inside dying a horrible death - whats Roy to do? And then the director wonders why Roy is waiting to do something. The example is a bit far out but the intent is the same. Change one thing and all that comes afterward is ruined and makes no sense. It stops being the story the author wrote. Directions are there for a purpose and are an integral part of the script. The director may know their stage better than the author but it should be the directors sole purpose to bring the script to life the best way possible in their venue, not change the story to suit their own desires & ideas. If they can't, they shouldn't be doing the script.

No POB I think you are right. I am not sure I have ever used the stage directions in the script. I read them but every house is different. Not that I think it is right but the playwrite has little or no control over the finished show. Screenwriters have no control over the finished film. They sell the script and the studio can do whatever they want with it. The nature of a play is that is is interputed by the company doing the show. I think this is the great part of theatre seeing what someone else makes of what was writen. That does not mean I think writers should just shut up and take it but it does happen all the time. I think fewer new plays would get done if writers were not open to suggestion on how to improve the script. I think the only time a writer can control it is with the first production, and then only if they put up the $$$ themselves.

Having been on both sides of the fence as a playwright and a director (sometimes on the same show), the only advice I have to offer is this:

There may be some things that are VITAL to your vision of the script and other things that are less so.  It's selecting the IMPORTANT moments and fighting for them, not nit-picking about everything that isn't "exactly" as you wrote it.