Based on comments by JRE and Joelogon, I'm guessing that the first story, "about a space war and time dilation", is "End Game", a novelette by Joe Haldeman, one of the shorter works on which his novel The Forever War is based.
The second story, with "eagle and deer metaphors", seems to be "Time Deer", a short story by Craig Strete, which was published in Worlds of If, November–December 1974, available at the Internet Archive.
An elderly Native American man scheduled to put into a nursing home by his son takes some time to commune with nature.
Excerpt (deer metaphor):
But the deer could not leave. She went a little distance and then turned and came back. And the old man was moved because he knew the deer had come back because the boy knew how to look at the deer.
And the boy was happy because the deer chose to favor him. And he saw the deer for what she was. Great and golden and quick in her beauty.
And the deer knew that the boy thought her beautiful. For it was the purpose of the deer in this world on that morning to be beautiful for a young boy to look at.
And the old man who was going someplace was grateful to the deer and almost envious of the boy. But he was one with the boy who was one with the deer and they were all one with the Great Being above. So there was no envy, just the great longing of age for youth.
Excerpt (eagle metaphor):
The old man had taken liberties in his life. He'd had things to remember and things he wanted to forget. Twice he had married.
The first time. He hated the first time. He’d been blinded by her looks and his hands had got the better of him. He had not known his own heart and not knowing, he had let his body decide. It was something he would always regret.
That summer he was an eagle. Free. Mating in the air. Never touching down. Never looking back. That summer. His hands that touched her were wings. And he flew and the feathers covered the scars that grew where their bodies
He was of the air and she was of the earth. She muddied his dreams. She had woman's body but lacked woman's spirit. A star is a stone to the blind. She saw him through crippled eyes. $he possessed. He shared. There was no life between them. He saw the stars and counted them one by one into her hand, that gift that all lovers share. She saw stones. And she turned away.
He was free because he needed. She was a prisoner because she wanted. One day she was gone. And he folded his wings and the earth came rushing at him and he was an old man with a small son. And he lived in a cage and was three years dead. And his son was a small hope that melted. He was his mother's son. He could see that in his son's eyes. It was something the old man would always regret.
But the deer, the young boy, these were things he would never regret.
The third story has been identified by SJuan76 as "Precious Artifact", a short story by Philip K. Dick, originally published in Galaxy Magazine, October 1964, available at the Internet Archive.
Organic Marble has found an anthology containing the first two stories; namely, the 1976 anthology Nebula Award Stories 11 edited by Ursula K. Le Guin.