Is it permissible for a traveler to Dammam, who intended to visit his father, to change his intention there to perform Umrah, and when should he enter into a state of Ihram, in terms of time and place?

If you travel to visit your father in Dammam and then wish to perform 'Umrah (definition), it is not a condition to stay in Dammam for three days; rather, you can go for 'Umrah whenever you wish. You should enter into ihram (definition) from the miqat (definition) for the people of Dammam, which is Qarn al-Manazil (As-Sail al-Kabeer). The general rule is that whoever comes intending 'Umrah must enter into ihram from the miqat. So, the miqat for the people of Egypt is Al-Juhfah or Rabigh. However, if you are going to another city like Dammam, it is permissible to delay entering into ihram and then enter into ihram from the miqat of the city you have reached.