In 1984, what are some internal and external conflicts?
Well, you certainly have a lot to pick from! I think just looking at the first chapter establishes the central internal and external conflict that are focussed on Winston Smith himself.
Firstly, it is clear that Winston Smith is a man who is in external conflict with the world of Big Brother. He deliberately breaks rules and regulations in secret that he knows will end in either his death or imprisonment. Consider what he says when he opens the diary:
The ting that he was about to do was to open a diary. This was not illegal (nothing was illegal, since there were no longer any laws), but if detected it was reasonably certain that it would be punished by death, or at least by twenty-five years in a forced-labour camp.
We are presented with a world that is tyrannical in its laws or the absence of them. Winston, by deliberately transgressing those laws, is immediately placed in conflict against the society he is in.
When it comes to internal conflict, it is Winston's desire to connect with someone else and share his feelings and what he is thinking about this society in spite of the harsh regulations and punishments that would occur if he did so that places him in internal conflict. Note what he says about O'Brien:
But at any rate he had the appearance of being a person that you could talk to if somehow you could cheat the telescreen and get him alone.
Winston desires to find the strength to reveal himself, but that places him in a massive internal conflict as he struggles to do what he has learnt instinctively:
To dissemble your feelings, to control your face, to do what everyone else was doing, was an instinctive reaction.
These then are two central conflicts that dominate the rest of the novel - Winston Smith's external conflict with the society he lives in and then the internal conflict he faces within himself as he struggles to find the bravery to find somebody to connect with.
Most of the internal conflicts arise from Winston's unhappiness with his life, and his suspicions that it is the Party that is the cause. At the beginning of the novel he is absolutely miserable, and that misery is mostly caused because he hates the Party and feels like he is the only one. He cannot be happy with it--it is an interna, Man vs. Self issue (even though his unhappiness is caused by the Party, Winston is conflicted with his angst about it). He struggles each day to even have motivation to get up in the mornings. He wishes so badly to know more--more people who feel the same, more about the history of the Party, and more about what causes true happiness.
So, internal conflict comes from Winston himself. After he meets Julia, he is conflicted constantly about his paranoia of being caught. It is always there, like a haze over his happiness. He is also internally conflicted about whether or not to make himself known to O'Brien; his fear of being caught battles with his desire to be part of a larger group of rebels.
The external conflict comes from the fear and repression that the party puts on its members. They are constantly watched by Big Brother, which leaves them living in continual fear of punishment for rebellion. They are even afraid to sleep, as their subconscious minds have betrayed them as they were sleeping. The party maintains that external fear through contstant examples of punishment, encouraging others to turn neighbors in, and propaganda.
Other external conflicts come at the end with Winston's torture and the slow deterioration of his body, and accordingly, his mind. The torture techniques appplied are external conflicts, that stem off of his internal fears of losing his mind, losing his love for Julia, and giving in to his worst fears.
I hope that those thoughts help to get you started; good luck!