1) largest area. According to Wikipedia's list of largest empires, the largest thalassocracy or colonial empire was the British Empire about 1920 with 3.35 million square kilometers or 13.71 million square miles, 23.84 percent of the world's land area of 148,940,000 square kilometers or 57,500,000 square miles.
2) longest lasting. The first Huang di of China took the title in 211 BC and the last Qing dynasty Huang di was deposed in 1912. Thus it can be calculated that the Chinese Empire lasted for 2,132 years. But the major Chinese dynasties ended in bloody civil wars often resulting in many millions of deaths and fragmentation of the realm often lasting decades or centuries. Thus it is hard to see government continuity between major dynasties, and it is common to refer to each major dynasty as a separate empire.
The Roman realm was a kingdom, republic, and empire lasted from sometime about the traditional foundation date of 753 BC, or the usual date of the foundation of the Empire in 27 BC, until the fall of the western Roman Empire in 476 or 480 AD (about 502, 506, 1,228, or 1,232 years), or the capture of Constantinople by the Fourth Crusade in 1204 (about 1230 or 1,956 years), or the capture of Constantinople by the Turks in 1453 (about 1,479 or 2,205 years), or the capture of the Morea by the Turks in 1460 (about 1,486 or 2,212 years), or the capture of Trebizond by the Turks in 1461 (about 1,487 or 2,213 years) or the fall of the Holy Roman Empire in 1806 (about 1,832 or 2,558 years).
See also here:
3) a) Largest total population:
By 1913, the British Empire held sway over 412 million people, 23% of the world population at the time,2
3) a) Largest percentage of the world's population:
Many sources say that the Achaemenid Empire in 480 BC ruled 44 percent of the world's population. But that is disputed here, in post # 12.
Post number 16 gives more accurate figures for various realms including a more accurate (hopefully) list of the ten historical empires with the largest percentages of the world's population.
1) Qing (1800): 38-39%
2) Tang (750): 36%
3) Song (1100): 35%
4) Ming （1600）: 33%
5) Mongol Empire (1300): 29-30%
6) Han (1 CE): 29%
7) Sui (600): 29%
8) Republic of China (1915): 27%
9) Roman Empire (160): 26%
10) British Empire (1922): 25.5%