Практически все 3 союза можно употребить в каждом из предложений.
1) He couldn’t play due to his injured shoulder.
2) She got the job owing to her excellent qualifications.
3) We couldn’t eat outside due to the awful weather.
4) She had to stay at home because of her broken leg.
5) The flowers died because of the dry weather.
1) Он не мог играть, из-за своей травмы плеча.
2) Она получила работу, благодаря своей отличной квалификации.
3) Мы не могли поесть на свежем воздухе, из-за ужасной погоды.
4) Ей пришлось остаться дома, из-за сломанной ноги.
5) Цветы завяли, из-за сухой погоды.
№1 ответ: 1)True (...have reached the five extreme points on the earth: the North Pole (three times), the South Pole...)
№2 ответ: 3)Not stated
№3 ответ: 2)False (When he was just 15 he went on his first expedition. Fyodor crossed the Azov Sea in a fisherman’s boat. Later he studied and graduated from the Odessa Naval College...)
№4 ответ: 2)False (He followed the routes of Vitus Bering,но документов не находил)
№5 ответ: 2)False (...he undertook most of his expeditions alone)
№6 ответ: 2)False (In 1990... trip to the North Pole...observed his own physical and psychological condition)
№7 ответ: 2)False (In 2016, at the age of 65, Fyodor Konyukhov set a new record – for a solo nonstop round the world flight in a hot air balloon. He never stepped on the ground during the whole flight)
№8 ответ: 2)False (Besides travelling, Fyodor Konyukhov writes poetry and fiction, paints pictures and composes music)