Short answers, pulled from the story.
Wallachia consolidated as an independent principality after 1330, when Basarab I decisively defeated Charles I of Hungary at the Battle of Posada. Basarab had first appeared in Hungarian records in 1324 as a voivode paying tribute, but by the end of the 1320s he had expanded his authority across both sides of the Olt River.
Wallachia was forced to accept Ottoman suzerainty for the first time in 1417, after Mehmed I captured the ports of Turnu Măgurele and Giurgiu. That suzerainty, with interruptions, lasted until the mid-19th century.
Transylvanian Saxon merchants, angered by Vlad III's border policies, distributed propaganda portraying him as a drinker of blood. Those stories spread into Germany and throughout the West, eventually inspiring the main character in Bram Stoker's 1897 Gothic novel Dracula.
Abolition came in stages between the 1840s and 1856. The earliest law, in March 1843, transferred state-owned slaves to local authorities. The Wallachian Revolution of 1848 placed emancipation on the Provisional Government's agenda. The law of February 1856 finally emancipated all remaining slaves and granted them the status of taxpayers.
A legal loophole in the 1859 elections allowed one person to run in both Wallachia and Moldavia simultaneously. Alexander John Cuza won in Moldavia on the 5th of January 1859 and was voted prince of Wallachia on the 5th of February, effectively uniting both principalities. The union adopted the name Romania in 1862 and became the Kingdom of Romania in 1881.
Wallachia derives from walhaz, a term Germanic peoples and Early Slavs used for Romans and other speakers of foreign languages. The same root produced the names Wales, Cornwall, and Wallonia. Romanians themselves called the principality Țara Românească, meaning Romanian Country or Romanian Land, and rarely used the exonym Wallachia.