1. Yes Jessica is Baron Harkonnen's daughter. Jessica had a Bene Gesserit mother who had an assignment to breed with Baron Harkonnen to collect his genetics as another one of the 1000 steps towards producing the male Kwisatz Haderach. Historically when this was done, the Bene Gesserit mother gives birth, and the Bene Gesserit community raises the child. The child has no idea who her mother or father is. They're essentially a Bene Gesserit orphan raised by the Bene Gesserit. This was Jessica's situation. Her father was Baron Vladimir Harkonnen, but she had no idea of this fact. Another bit of trivia - Jessica's mother was Gaius Helen Mohiam, the old reverend mother who tested Paul with Gom Jabbar to see if he was human in Dune 1. Jessica also has no clue that Mohiam is her mother.

2. Yes, there is a secret stash of atomics in the books. It didn't play a major role other than they used it to breach the shield wall so that they could drive their worms through it to the plains of Arakeen to fight Emperor Corrino. Every great house in the universe has a stash of atomics. They're referred to as the "family atomics." The great convention (basically the rules that every great house agreed to abide by after they defeated the thinking machines 10,000 years earlier) prohibited the use of atomics against any living human. Every house retains atomic weapons though, and they help enforce obedience to the great convention through the fear of mutually assured destruction.

The only time in the history of the emperium when atomics were used against humans in contravention of the great convention was when a rebel great house upset with the Corrino empire tried to use atomics to wipe out the Corrino family with atomics. At that time the capital of the emperium was on Salusa Secondus (which is now the wasteland prison planet where the Sardukar are trained). The atomics attack turned Salusa Secondus into a wasteland planet, but the attack was not successful in killing the emperor or a big chunk of the Corrino family. After the attack, the Corrinos moved the capital of the Empire to the planet Kaitain and built the capital city of Corrinth.

Back to Paul and his use of atomics - he technically didn't violate the great convention when he used the family atomics as a giant EMP bomb to breach the shield wall because he didn't use the atomics agains humans. They were just used against the protective shield wall. However, nobody was happy about this because even though it technically didn't violate the letter of the law of the great convention, it was definitely against the general spirit of the great convention. It was a technical loophole.

3. Yes, Paul and his fremen go on a jihad against all the great houses in the Universe who won't accept him as the new emperor. This is largely not covered in the 6 original books. It just happens in the gap between book 1 and book 2. By book 2, the jihad is substantially over, and Paul is more or less stable in his role as emperor of the known universe. When Frank Herbert's son, Brian, came back and started writing prequel and gap-filling books based on the notes and partial manuscripts of his father, Brian wrote a gap-filler book that gives the story of the jihad that fills in the 12 year time period between the original book 1 and book 2.