1 One moment, please, unfortunately Europeans dynastic links are a great mess. So I think it's better a little background:
A) The Bourbons were the Royal Dynasty of France after Religion Wars in XVI Century. The French Succession Law is very strict: this is based on a Salic Law, allowing only Catholics Kings, not including the possibility of an abdication and declaring the present law unchangeable (only God in person can change the Law).
B) In 1700, following the (manipulated) testament of Charles II of Spain, a Bourbon became King of Spain, diving the family in French and Spanish Bourbons (and technically also Parma, Naples,... but now this is irrelevant). In change of this, after Spanish Succession War, Spanish Bourbons renounced their succession rights on French Crown with the peace Treaty of Utrecht.
C) In 1830 Bourbon Monarchy was overthrowed during the July Revolution and replaced by a cadet branch, the Orleans.
D) In 1833 Ferdinand VII of Spain changed Spanish succession law in favor of his daughter Isabell II against the male Salic line of his brother Charles. This is the beginning of Carlists Wars, that Carlists lost.
E) In 1848 Orleans are overthrowed by republicans: now in France there are two Pretendets, the Legitimist Bourbon Line and the Orleanist one.
F) In 1870, after a failed attempt to restore the Monarchy, the last Legitimist Pretendent Henry, Count of Paris, who is childless, agrees to declare the Orleanist Pretendent as his heir.
G) After Henry's death in 1885, the most part of Legitimists merges with Orleanist under old Orleanist and now Legitimist-Orelanist United Line.
H) But a minority, leaded by Henry's widow, opposes, arguing that the Treaty of Utrecht violated Succession Law (if abdication is forbidden, also the rejoice of their rights is) and so the Crown was of the last Spanish male Bourbon Line: the Carlists. This minority is called White Legitimists.
Meanwhile France becomes a republic with a President that has more power than a King.
So, when I said "Legitimist" I thought about main Legitimist Line, so Orleanist Line (Points F and G). Its Pretendent at time, John III, was strongly linked with Action Francoise and protested when AF was excommunicated by the Pope Pious XI in 1924 and Maurras himself pledged support to John's father, Philip VII, in 1909. Only problem for him is that John's son, Henry VI, was anti-fascists so could be some problems when John III will die in 1940.
2 Well, actually old Italian Succession Law was based on Salic Law so woman are excluded (and Filiberto's first daughter is born in 2003, so too late). Vittorio Emanuele IV has only sisters and so his father Umberto II. Umberto's grandfather, Umberto I, had only one son (Vittorio Emanuele III) so the next in line is a member of cadet branch of Savoia-Aosta, directly linked to Vittorio Emanuele II, first King of modern Italy, thorough Amedeo I, briefly King of Spain, and Emanuele Filiberto, General during World War I. Emanuele's first son Amedeo died during World War II with only daughters, so the heir is his brother Aimone, briefly King of Croatia, only son, Amedeo, Duke of Aosta. It's possible but would be a little traumatic.