Short answers, pulled from the story.
The Bourbon Restoration began on the 6th of April 1814, when Louis XVIII returned to the French throne after Napoleon's defeat. It ended formally on the 2nd of August 1830, following the July Revolution that forced Charles X to abdicate. Louis-Philippe, Duke of Orleans was elevated to the throne on the 9th of August 1830.
The Charter of 1814 was the constitutional document that established France as a constitutional monarchy under Louis XVIII. It created a bicameral legislature with an appointed Chamber of Peers and an elected Chamber of Deputies, restricting the vote to men paying at least 300 francs a year in direct taxes. Just one percent of the population could vote.
The White Terror was a wave of royalist violence following the Second Restoration of 1815. Unofficial royalist groups known as the Verdets killed around 200-300 people and forced thousands to flee. About 70,000 government officials were dismissed, along with 15,000 army officers and between 50,000 and 80,000 civil servants.
Charles X was overthrown because his July Ordinances of 1830 dissolved the Chamber of Deputies, suspended press freedom, and restricted the franchise, triggering the July Revolution. A series of bad harvests between 1827 and 1830 had caused severe economic hardship, and 221 deputies had formally condemned his government in March 1830. He abdicated on the 30th of July 1830.
The liberal bloc in the Chamber of Deputies grew from 17 seats in 1824 to 180 in 1827 and 274 by 1830. Opposition societies coordinated candidates and voter registration, adding 18,000 new voters to the rolls of 60,000 before the 1827 election. A growing liberal press in Paris amplified opposition to the crown.
Adolphe Thiers led a meeting of wealthy liberal journalists and newspaper proprietors in Paris on the 10th of July 1830, three weeks before Charles X issued his July Ordinances. The group agreed to publish fierce criticism of the king's expected decrees to mobilize public opinion. When Charles issued the Four Ordinances on the 25th of July, the liberal press responded exactly as planned, helping trigger the revolution.