1.Who do you think was the rightful heir to the English throne after the death of Henry I. His daughter Empress Matilda or his nephew Stephen ?
Succession wasn't as solid as that during that era. Henry himself had an older brother (Richard, Duke of Normandy) alive when he became King. Richard was the eldest surviving child of William the Conqueror, but was passed over in the English succession in favour of second son, William II. Henry I seized the crown when William died.
Anglo-Saxon tradition did not allow for female inheritance, but I believe some of the Anglo-Saxon kingdoms (I believe in particular Mercia) allowed for men to inherit through their wives and mothers; the idea being that if you married the daughter of a King who had no sons to succeed, then you or your sons might succeed.
This kind of idea is seen within the succession to some noble titles in Britain at the time as well.
At the same time, though, Matilda was named heir by her father, the King, and had his great council swear to recognize her as such.
So... it's really not as simple as one or the other was the right heir. Matilda was acknowledged as Henry's heir during his lifetime, but Stephan was able to use his position at the time of Henry's death and the culture and tradition of England to his advantage.
2.And do you think that Empress Matilda ever really had a chance to win the war against Stephen.
Yes. The Anarchy lasted for 20 years before the peace negotiations. While it ended with Stephen on the throne, Matilda's son was recognized as his heir. A war doesn't last for 20 years if both sides don't have a chance.
3.And would you say that Empress Matilda ended up as the winner in the end considering that it was her son who became King after Stephen ?
The Anarchy ended in stalemate. After 20 years of civil war and the death of his heir Stephen needed a solution... at least a temporary one. It's very possible that Stephen recognizing Henry as his heir (after Eustace's death) was just a move to allow for a temporary peace until a better solution came up - like the planned assassination of Henry.
4.What do you think was the biggest mistake Empress Matilda made after the battle of Lincoln when she captured Stephen ? ( Well i guess it was her half brother Robert that captured him. )
The big mistake was that they captured Stephen. If he had died at the Battle of Lincoln they would have been done with it. But with him alive... their options were more limited, and executing him wasn't one of them.
5.Do you think that if it had not been for Stephens wife Matilda of Boulogne rising her army against Empress Matilda and taking her half brother Robert. And forcing Empress Matilda to trade King Stephen with Robert. That the Anarchy would have ended in a different way ?
There are so many "what ifs"... so many turning points in the Anarchy that if done differently could have changed the course of the war. Heck, that's the reality of history. If Stephen hadn't been taken a prisoner after the battle, the Anarchy might have gone differently - it certainly would have ended differently had he been killed at the Battle of Lincoln instead of taken prisoner. Had Matilda of Boulogne not taken an army against Empress Matilda and captured Robert of Gloucester, the war likely would have ended differently. Had Eustace of Boulogne not died, had the assassination plot of Henry been successful... the whole thing may have gone differently had Matilda not been pregnant and on the Continent when her father died.
