"Ok. I need another 40k history lesson
."
There is a common misperception that Rogue Trader was set back in the Horus Heresy. In fact, 40K has always been set in the 41st millennium. The Horus Heresy was first explored in Epic: Space Marine. It has recently been the subject of numerous books. Although fans are now converting lots of Horus Heresy era armies, I don't think GW has ever published army lists or run events set in that time frame.
"So why did Hours go over to chaos? And how/why did the other Chapters went over with him? Was this ever described?"
Horus was badly wounded by an ultra-deadly alien weapon. He seemed to be near death, and in desperation, his legion handed him over to a "warrior lodge" on Davin. This was in fact a Chaos Cult. Horus recovered, but was seduced into Chaos in the process.
"Also, I thought that the Emperor got killed with his fight with Horus. No? Did Horus get killed also?"
NO! The Emperor lives on, enthroned on Terra. Although his body is wasted, his mind controls the Astronomican, the psychic beacon that guids Imperial ships through the warp. The Emperor slew Horus with a blast of psychic energy.
"It is said that the 20 Primarchs are 'sons' of the Emperor. That they were made under the Imperial Palace, but then they got 'lost'? How ??? You don't forget where you put cloning chambers like you forget where you put yer keys down, do you? And who did the cloning? The Emperor himself? Why?"
They WERE made on earth. The Emperor himself contributed genetic material, and probably was heavily involved in the process of cloning. There are hints that he may have bound energy from the warp into the primarchs. Why? If you are going to set out to reconquer the entire galaxy, you had better have some awesome generals to lead your troops! Also, creating them made it possible to create the Adeptus Astartes.
The infant primarchs, while still incubating in arcane machines were stolen from beneath the palace by Chaos. In a strange time-loop, Horus was there and unwittingly made the theft possible. (This was part of the strange stuff that happened too him on Davin while recovering.) The Chaos gods could not destroy the primarchs, so instead they were scattered throughout the galaxy. There is a hint that Horus may have accidentally killed one of the primarchs when they wre stolen. That might explain one of two missing primarchs/legions, but not the other.
"How may of the Primarchs survived after the Horus Hersey? Are they still around in the current edition of the game?"
No loyal primarchs are known to be still living. However, several are rumored to be waiting, somewhere, perhaps outside of time, and will return for the final battle with Chaos. Lion El'johnson, Leman Russ, Corax, Jaghetai Khan,and Vulcan all fall into this category.
Roboute Guilliman, Ferrus Manus, Sanguinius, and definitely dead. (Though it is said that Guilliman's wounds are slowly healing, even though he is in a stasis capsule!)
Early accounts state that Rogal Dorn is dead, and that his skeleton is in the possession of his chapter, the Imperial fists. But later ones say that although his ship was lost fighting a Chaos fleet, only his fist was ever found, not the rest of his body. So there is a tiny chance that he survived. My own chapter, the Hammerhands, believes this, but I think GW's canon Imperial Fist chapter and its descendants believe he is dead.
As for the primarchs who turned to chaos:
Horus himself is dead. Nighthaunter is dead, and apparently welcomed it. Alpharius is dead, but read the Horus Heresy book LEGION for more on that. Angron, Mortarion, Magnus the Rad, Lorgar, Perturabo, and Fulgrim all becam daemon princes. On top of that, Fulgrim was already possessed by a daemon before being elevated to princedom.
"They also say that the Astartes was with the Emperor during the Great Crusade, and that lasted over 200 years. How long does the Primarchs live for?"
Astartes can live for hundreds of years, the exact amount varies by chapter. The Primarchs seem to have been immortal. None ever died of old age. They either died in battle, or disappeard. The certainly live at least 1000 years, because that is when the last one was lost or killed.
"Who did the second founding of the sub-chapters?"
The Adeptus Mechanicus, at the direction of the High Lords of Terra, conducts additional foundings of Space Marines. There have been over 30 foundings so far. The Second founding was different, in that it involved breaking up the existing Legions into smaller Chapters of 1000 marines each. Thie was Robout Guilliman's idea, and was done according to his Codex Astartes.
"Is there a good fan site around that has the history all laid out?"
Check out Bolter & Chainsword for a forum dedicated to this kind of thing: bolterandchainsword.com