Hi,
Generally, I agree with what has been said, but I would also like to add a comment.
speak with - I tend to view this as a feature of N. American English.
speak to - This is more common in Canadian English, and (as far as I know, unless things have changed in my long absence) in British English. Whether or not the other person also spoke is usually obvious from the context or simply unimportant.
Best wishes, Clive