You asked it, you got it. Here is the solution
1. Called the "Solomon of the century" because of his wisdom, he was a powerfull ruler who retired to become a monk, before being elected anti pope, and resigned 9 years later to quell the old dispute with Rome. What are his names and country of origin?
Amédée VIII, Duke of Savoy, Pope Felix V.
Gagliaudo was the only one to find it. Although he said he was half French , half Italian :shakehead
2. After the defeat of Japan in 1945, the Americans banned all martial arts. What was the first to be authorized again, and why?
Aikido, because its the most pacifist one. North King got it.
3. What did Richelieu used as a model when he created lacadémie Française?
Lacadémie florimontane, created in Savoy in 1607.

No one found it. You should read the only history article I wrote...
4. What are Napoleons Marshals who were killed during a battle (including death because of the wounds received during the battle).
Bessières, Lannes, Poniatowski. Ney and Muret were executed, and Brune was killed during a riot, so they do not count as it was not in battle.
5. What is the percentage of French casualties during the Indochina war, relatively to American casualties during the Vietnam war ?
87000 French to 58000 Americans, this means 150%. One answer x2 and got half a point.
6. Why is the highest speed limit 110 km/h in Brittany, when is it 130 km/h in the rest of France? (Yes, this is really an history question).
Because when Brittany joined France through a marriage, a condition was that Brittany will not have taxes on the roads, and thus there is no motorway in Brittany (although they are 2x2, they are considered "normal" roads). No one answered correctly.
7. How many famillies have seated on the Imperial throne of Japan?
Only one. Although the emperor seldom had any real power and was often a pupet, there have been no dynastic change in Japan
8. Give the name of 5 religious military orders of the middle ages.
Knight templars, Hospitaliers or St John, or Knights of Malta), Teutonic Knights, Santiago (or Saint Jacques of th Sword), Porte-Glaive, Alcantara, Calatrava, Brother of th Sword (in French "Porte-Glaive"). When someone gave the same order with different names (such as Hospitaliers and St John), I counted only one.
9. What is the main reason why catharism was considered an heresy?
No one really got it, although some gave a start of answer. Cathars believed in manicheism. The spiritual world was from God, and the material world from the Devil. Thus, they denied Jesus was flesh, and said he was only spirit (or he would have touched by the Devil).
The heresy was they denied Jesus was God made man.
10. What was the first engineer school created in France? And when?
"Ponts & Chaussées", (bridges and roads). Created in 1747 by the king, and reorganized in 1804 by Napoleon. The corps of engineers was created in 1716, but the school was created 31 years later.
Polytechnique (created in 1795 by Napoelon) was a trap...
Pawpaw, your turn