I saw it for the second time yesterday. I too had read the book before I saw the movie, so it was a spoiler for me. I knew I should not read the book first, but my dark side took over. LOL.
Major spoilers ahead...............
To address some of the questions- the Jedi's had certain powers but they were not 'God's. They could sense something negative happening, but it does not mean they would sense it every time. Also they could not tell the exact origin of it. They could only suspect that something was wrong somewhere. They were busy doing their duties and were caught unaware.
Although Anakin was supposed to be the chosen one, the Jedis never fully trusted him, with the exception of Obi Wan. In spite of saving the republic many times in wars, Anakin never got the full support or appreciation from the Jedi. Palpatine used it to turn him to the dark side. The senior Jedis needed to help Anakin overcome his weaknesses rather than keep a distance from him.
Yoda sensed the anger and fear in Anakin but he went along with the decision to train Anakin probably because he had no idea how far in the wrong direction those qualities would take Anakin. However, Yoda was the only one that had the bad feeling about something as early as in the Phantom Menace.
Further, Yoda and others were unaware of the fact that Senator/chancellor Palpatine was Darth Sidious- the Sith they were looking for. In fact it was Anakin who guessed it right because he was close to Palpatine. Unfortunately Anakin was young, vulnerable, and dreadfully afraid of losing his loved ones. He was genuinely supportive of the Jedi but the fear got the best of him. Palpatine used the trust the Jedis had in Anakin to destroy them. Had he sent Count Dooku, they would have faught him.
Why did Vader not recognize Leia as his daughter? Nobody knew, until the twins were about to be born, that Padme was carrying two babies. Vader did not know that Padme had given birth. At the funeral they made sure that Padme looked pregnant. That protected the babies for sometime because very few knew they had been born. If Vader felt later that she did give birth before dying, he assumed that he had a son as his only child (Luke Skywalker- the name made it easy to track him down, didn't it?). He did not suspect the twin sister until Luke's thoughts betrayed him in Return of the Jedi. Darth Vader did not know that Leia was his daughter. However, in episode 4 (Original Starwars movie) he always saved her life whenever Tarkin tried to kill her, by saying that she may be useful to them. So I think deep down somewhere he had soft, parental feelings for her.
The force was strong in both Luke and Leia but they had very different upbringings. Leia was inclined toward politics, while Luke was a warrior, which made it easy for him to develop the Jedi abilities. Without the training Obi-Wan gave him, he could not have developed, however. In one of the Starwars books (they start after ROTJ) Leia had those abilities and Luke was training her to become a Jedi. However, her natural inclination was always political. Remember who her mother was? (Senator Padme Amidala)
It will be wonderful to have episode 3.5 in which we see the children Luke and Leia grow up.
In ROTJ when Luke asked Leia if she remembered her real mother, she said "I little; images really". So I had expected to see Padme alive for a few years after giving birth to the twins. However, since I read the book first, that suspense was gone too. The only explanation I have for Leia's answer is- she misunderstood Luke's question. She may not have known that she was adopted.
In the post-ROTJ novels that came out, we read about Leia & Han Solo marrying, Luke creating/training Jedis in different parts of the galaxy, etc. Unfortunately the actors of the original trilogy are too old now. It would make more sense to create a movie between Episodes 3 & 4.
About killing of the younglings- this was the ultimate atrocity, and it showed how evil Palpatine really was. He did not try to convert the young ones to the dark side- something he could have done easily, but he would not take that risk. It was easier to kill them using Anakin because they trusted master Anakin. Very very evil! I could not help feeling sorry for Anakin because he was a young man who honestly wanted to do the right thing but somehow he got to the point from where there was no return. His downfall really began when he killed the women & children of the sand people (or Tusken raiders?) in Attack of the Clones. That action sowed the seeds of his destiny.
Vash