I don't think the battle is definitely canon. I imagine whether or not Raiden and Kahn had a battle during MK3 is one of those things that's up to interpretation.

Way I personally see it, is before the final battle between Liu Kang & Kung Lao against Kahn was there was a brief confrontation between Raiden and Kahn....Raiden trying to intervene, fearing Liu wasn't ready to best him. They had a quick fight, but Raiden pulled back...unable to defeat him.
The reason, I think, Raiden was unable to defeat Kahn...aside from giving up his god-hood....was Sindel. My theory...just my theory....is that until the realms completely merged, Kahn needed Sindel as his bride because she was his link to Earth. And as long as she was his bride he was...more or less...unbeatable.
The reason Liu Kang was able to overcome Kahn, as opposed to Raiden, was because by then Sindel had broken free of Kahn's control so his link to Earth broken...making him vulnerable.

My main reasoning for this scenerio is it places importance back on Sindel and makes her turning against Kahn relevent to the overall plot and not just a random event.

So back to original question, I think whether Raiden fought Kahn or not is up to you because it's never been confirmed as canon. How and why Raiden did not destroy Kahn, again, is up to you.

Good question. I havn't a clue. But Raiden did state before MK3 that he cannot interfere any longer and after MK3: "Shao Kahn's defeat at the hands of Earth's warriors. So whether or not Raiden fought Kahn is unkown. Probably not, he probably held of some of Kahn's henchmen while Kang fought off Kahn. But nothing is certain.

I doubt it, because it is against the rules of Mortal Kombat for a God to fight. And also, because it was Liu Kang who actually BEAT him, so my answer would be no, but it's just my interpritation.

well in mortal kombat trilogy which is considered mortal kombat 3 storywise raiden is in mkt. correct if im wrong.

Thanks guys! I wrote up what I needed to make a mention and some kind of description for what happened with Shao Kahn during the end of MK3. The thread can be... Wait, that's my job, I don't have to ask anyone.