In dictatorships such as Nazi Germany or North Korea. Are members of the inner circles or expert advisors allowed to disagree or offer advice that contradicts the Dictator? What happens if they do.

You didn't mention Stalin's Russia, but as one of the most rigid and despotic dictatorships of the 20th century it deserves a mention. Stalin's various minions and stooges were certainly very cautious about disagreeing with him, because after he established his complete hammerlock on power in the mid-1930s, he could have these men or their families tortured and killed for any reason, or for no reason, and often did. However, opposition did happen, and Stalin's reaction was unpredictable. Men who challenged him might be demoted, they might simply be ignored, or in some cases they might actually persuade him, the latter becoming more true during WWII after the disasters of 1941-42 showed Stalin and everyone else that he wasn't infallible.

Consider the following exchange between Stalin and general (later marshal) Konstantin Rokossovsky, who had already been imprisoned and probably tortured during the Great Purge, but then reinstated when the war with Germany produced a huge demand for capable officers.

In a meeting in May 1944 to plan the great counterattack that would clear all Soviet territory of Germans, Stalin suggested a plan to do a single massive attack, but Rokossovsky thought two separate attacks would be better. They argued and Stalin sent the general out of the room to think it over. Rokossovsky came back in and stuck to his guns, and was sent out again, this time also to be accosted by Molotov and Malkenkov, two of the grimmest of Stalin's murderous cabal. They asked him if he knew who he was arguing with and told him he'd have to give in. The implied threat would have been obvious to a man who had already fallen afoul of Stalin's purges, but when he reentered the room, with almost unbelievable courage, Rokossovsky still told Stalin that "two thrusts [were] more advisable." And Stalin gave in, and adopted Rokossovsky's plan, which turned out to be a great success and played a part in earning Rokossovsky a promotion to marshal.

We are aware of other examples of Stalin responding tamely to people who stood up to him, but it was perhaps most likely that someone would be shuffled off to an obscure post in the hinterland, and not at all unlikely that someone would simply disappear into the basement of the Lubyanka and never emerge alive.