What is the ruling on traveling to perform 'Umrah and enroll in university while my father is on his deathbed, knowing that my siblings will take care of him?

If your father wishes for you to stay by his side, this takes precedence over you going for Umrah (definition) and applying to the university; due to his immense right to dutifulness and connection. Imam Bukhari and Imam Muslim narrated from Abdullah ibn Amr (may Allah be pleased with them both) who said: "A man came to the Prophet (peace and blessings be upon him) and asked his permission to participate in Jihad. He said, 'Are your parents alive?' He replied, 'Yes.' He said, 'Then strive in their service.'" However, if he permits you to go and does not need you to stay with him, then it appears that you should travel to earn reward, seek knowledge, preserve the money you have spent, bid farewell to your father, ask for his forgiveness and pardon, and advise your siblings concerning him and to follow the Sunnah (definition) in his funeral procession and burial should Allah Almighty take his soul.