Short answers, pulled from the story.
Italian Eritrea was formally established as the Colony of Eritrea in 1890. Its origins trace to 1869, when Giuseppe Sapeto negotiated the purchase of Assab Bay on behalf of the Rubattino Shipping Company, with Italy taking government control of the territory in 1882.
The Treaty of Wuchale was signed in 1889 between Italy and King Menelik of Shewa, recognizing Italian control over the Eritrean highland regions of Bogos, Hamasien, Akele Guzay, and Serae. The Italian version of the treaty made Ethiopia an Italian protectorate by requiring it to conduct foreign affairs through Italy, while the Amharic version contained no such clause. Emperor Menelik II denounced the treaty in full, and the resulting war ended with Italy's defeat at the Battle of Adwa.
The Italian settler population in Eritrea grew from around 4,000 during World War I to nearly 100,000 at the start of World War II. In Asmara specifically, the 1939 census recorded 53,000 Italians out of a total city population of 98,000, making Italians 54% of the capital's residents.
Asmara was nicknamed Piccola Roma, meaning Little Rome, because of its Italian architecture, wide piazzas, coffee bars, and planned city layout with designated zoning and treed boulevards. During the years it was being built, Asmara had more traffic lights than Rome itself. Historian Gian Luca Podesta wrote that the city had become in practice an Italian city.
The Eritrean Ascari were indigenous Eritrean colonial troops who served in Italian military operations, described by Italian Marshall Rodolfo Graziani and officer Amedeo Guillet as the best Italian colonial troops. After World War I, service with the Ascari became the primary source of paid employment for Eritrean men. During the Italian invasion of Ethiopia in 1936-40% of eligible Eritreans were enrolled in these forces.
When the Allies captured Italian-held Eritrea in January 1941, the infrastructure was heavily damaged, and assets like the Asmara-Massawa Cableway were removed and sent to India and Kenya as war reparations. After Italy's armistice in September 1943, Eritrea came under British military administration. Under United Nations supervision from 1951, Eritrea became an autonomous part of Ethiopia in September 1952, before achieving full independence in 1991.