Gandalf is a maiar, a lesser angel, clothed in a mortal form and sent down to guide the people of middle earth as a wizard, aka, Istari. He is not a mortal man and does not have a biological family, his 'father' is the creator god, Eru Iluvatar, who created all the Valar and Maiar to aid him in creating the world.
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Drogo Baggins was his father and his mother was Primula Brandybuck. See Appendix C of The Lord of the Rings.
Aragorn's father was Arathorn II, fifteenth Chieftain of the Dunedain of Arnor. He died when Aragorn was two years old, after which Gilraen took her son to Rivendell to be fostered by Elrond.
Gandalf does not have a father as he is not a human, but a member of the wizard order, or Istari.
Her name is Arwen Evenstar, if you're talking about the Arwen from Lord of the Rings
first it's Aragorn and his father's name is Arathorn II
Thranduil is the Elven King of Mirkwood, and father of Legolas.
Yes, as the father of Legolas (a member of the "The Company of the Ring").
He was the Bagginses' gardener as his father was before him.