Short answers, pulled from the story.
Most historians agree that Gilgamesh governed the Sumerian city-state of Uruk during the Early Dynastic Period. Stephanie Dalley states that precise dates for his lifetime likely fall between 2800 and 2500 BC.
Archaeologists excavated a seal impression dated to circa 2600 BC in the Royal Cemetery at Ur. This artifact now resides in the National Museum of Iraq with an inscription reading Gilgameš is the one whom Utu has selected.
Sîn-lēqi-unninni composed the standard Akkadian version of the epic during the Middle Babylonian Period between 1600 BC and 1155 BC. The most complete surviving version rests on twelve clay tablets found in the Library of Ashurbanipal at Nineveh dating to the seventh century BC.
Ishtar demanded Gilgamesh as her consort after he rejected her advances so she sent the Bull of Heaven which they killed offering its heart to Shamash. Enkidu died after dreaming of the Underworld following their victory while Tablet VII records Gilgamesh's death and Tablet VIII details his inconsolable grief.
Austen Henry Layard discovered the Akkadian text in 1849 AD within the Library of Ashurbanipal at Nineveh. George Smith produced the first translation in the early 1870s publishing the Flood story from Tablet XI under the title The Chaldean Account of Genesis in 1880.