The 4th story is "Born with the Dead", a 1974 novella by Robert Silverberg, which was the (unaccepted) answer to this old question. It was first published in The Magazine of Fantasy and Science Fiction, April 1974, which is available at the Internet Archive. Here's a description from Majipoor.com:
In the 1990s, doctors have discovered how to rekindle dead people, re-animating the bodies and minds. But the deads are different, aloof, unconcerned with the matters of warms — those still alive — and mostly keep to the Cold Towns. Jorge Klein finds that he cannot let go of his dead wife Sybille, and seeks her out obsessively, following her around the globe. This is just not done, but Jorge can't stop himself.
One interesting scene involves an African preserve set aside for vacationing deads, where they must leave the native animals alone and hunt instead genetically recreated extinct species — aurochs, ground sloth, quagga, passenger pigeon, dodo. Many aspects of the situation are explored, including the attitudes people of different cultures have towards death.
The 2nd story might be "Equinoctial", a 1977 novella by John Varley, which was the answer to this old question. It's part of Varley's Eight Worlds series, which has a Wikipedia page. It's not just a human soul, but a whole human body is encased in a nonhuman "Symb", and can then live in space. (The story is set in the rings of Saturn.) And female humans do give birth in space:
To gain enough useful mass to produce one baby, a Symb-human pair had to ingest almost a thousand kilograms of rock and ice. Only a tiny fraction of it was the chemicals needed to produce a baby. Then, to convert the mass to useful form, energy was required. The pair had to spend long hours in the sunlight.
The book containing the two aforementioned stories (well, the only one known to the ISFDB, which doesn't know everything) is The Arbor House Treasury of Great Science Fiction Short Novels, a hefty (x+768 pages) hardcover anthology edited by Robert Silverberg and Martin H. Greenberg, first published in 1980. (A 1989 edition was titled Worlds Imagined.) I try to find matches for your other two stories in this Arbor House Treasury.
The 3rd story seems to be "The Golden Helix", a 1954 novella by Theodore Sturgeon, also the answer to this old question; first published in Thrilling Wonder Stories, Summer 1954, available at the Internet Archive. Human space travelers are hijacked by powerful aliens and marooned on a green planet (the humans name it Viridis) with dangerous wildlife. These are evolved future humans, less hairy and angular than us, and multiple births are the norm with them:
"I always thought it was a silly kind of joke anyway," she said primly. "Judging virility by the size of a brood. There isn't any scientific basis for it. Men are silly. They used to think that virility could be measured by the amount of hair on their chests, or how tall they were. There's nothing wrong with having only three."
"Carl?" grinned Tod. "That big 'ol swashbuckler?" He let the grin fade. "All right, Ape, I won't let Carl see me laugh. Or you either. All right?" A peculiar expression crossed his face. "What was that you said? April! Men never had hair on their chests!"
"Yes they did. Ask Teague."
"I'll take your word for it." He shuddered. "I can't imagine it unless a man had a tail too. And bony ridges over his eyes."
"It wasn't so long ago that they had. The ridges anyway. Well—I'm glad you didn't laugh in front of him. You're nice, Tod.
The 1st story could just possibly be "By His Bootstraps", a 1941 novella by Robert A. Heinlein which was the answer to this old question; originally published (as by Anson MacDonald) in Astounding Science-Fiction, October 1941, available at the Internet Archive. It is a time-travel story, but I can't say that your description matches my recollection of the story very well.
At least, there is a hat in the story. From the Wikipedia plot summary:
Bob Wilson locks himself in his room to finish his graduate thesis on a mathematical aspect of metaphysics, using the concept of time travel as a case in point. Someone says, "Don't bother with it. It's a lot of utter hogwash anyhow." The interloper, who looks strangely familiar, calls himself "Joe" and explains that he has come from the future through a Time Gate, a circle about 6 ft (1.8 m) in diameter in the air behind Joe. Joe tells Bob that great opportunities await him through the Gate and thousands of years in his future. By way of demonstration, Joe tosses Bob's hat into the Gate. It disappears.