What was Sophocles' intention in writing "Oedipus Rex"?What issues or questions was he trying to present to the audience of his time?
Usually in answering questions about classical authors' intentions, the answer is "who knows?". Sophocles didn't leave us any information about precisely why he wanted to write the play - there isn't a foreword to the text by hm that explains what he was trying to do. So all we have to look at is the text. And that comes down to interpretation, which, as you know, can be very different depending on where you stand.
What are the themes then of Oedipus Rex - what is the play about? It's about never thinking you know the future, about fearing the gods, about how things creep up on us, about man's inability to control his fate, and about parents, children and how they don't actually "know" each other in any actual sense. So we can only presume Sophocles was interested in all of those things.
Another way of answering the question might be to look at the Oedipus myth: the story of Oedipus which Sophocles based his play on, and look precisely at the way that Sophocles adapts that into the play - that's another way to see what it is he was trying to do.
And of course, one more important answer to the question is that Sophocles' intention was to win money. Oedipus was entered into a Festival of Dionysus which was a big drama competition in Ancient Greece which gave huge prizes for the writer whose plays were considered the best. So that must also have been in his mind!