I don't know the answer to the first part of your question unfortunately, but as to what happened to Lodbrok's sons:

First of, only three of his son's were leaders in the Great Heathern Army: Ivar Ragnarsson ('Ivar the Boneless'), Halfdan Ragnarsson, and Ubbe Ragnarsson.

• Ivar Ragnarsson left the GNA in 869 and possibly returned to Scandinavia (where he was the ruler of a small quasi-independent "kingdom") or traveled on to Ireland.

• Halfdan Ragnarsson: Halfdan, or Hvitserk, was taken prisoner and executed in 877 after a lost battle.

Men Hvitserk, hennes sønn, hadde engang herja i Austerveg, da det kom en så stor overmakt mot ham at han ikke klarte å gjøre forsvare seg, og ble tatt til fange. Han valgte seg den dødsmåten at det skulle bygges et bål av mannshoder, og der skulle han brenne, og slik mistet han livet sitt. [at 18, in Norwegian].

"However Hvitserk, [Hvitserk's mothers] son, raided east, and so great were the odds against him that he failed to defend himself, and was taken prisoner. He chose that a bonfire of heads would be built, and that as a way of death, that there he would burn, and so he lost his life."

• Ubbe Ragnarsson: Ubbe was apparently killed in 878 at the Battle of Cynuit.

However, Ragnar Lodbrok had at least two other sons:

• Bjorn Ironside, who sailed to the Mediterranean and raided the Spanish coast, the south of France, and Italy before heading for home and living out his life as a rich Scandinavian "king".

• Sigurd Snake-in-the-Eye, legendary King of Denmark and (apparently) the predecessor of Gorm the Old.

The Ragnarssona þáttr also speaks of Eysteinn Beli, Jarl of Sweden, fighting against Eric and Agnar, two more sons of Ragnar. Apparently Agnar was killed and Eric taken prisoner and later killed.