You may be thinking of Keith Laumer's 2002 collection Odyssey comprising two novels and several shorter works, including the two stories mentioned below.
The first part of your question could be describing the novel Galactic Odyssey as suggested in the answer by Barnaby. (A shorter version of Galactic Odyssey, titled "Spaceman!", ran as a 3-part serial in If, which is available at the Internet Archive: Part one, Part two, Part three.) Here is the Wikipedia synopsis:
Down-on-his-luck college dropout Billy Danger shelters from a sleet storm in what he thinks is a corn silo, but which turns out to be a space yacht containing three upper-class hunters from a planet located halfway across the Milky Way. They take him on as a gun-bearer, but after landing on a desert world known as Gar 28, both of the male hunters are killed by their prey. Billy is left alone with the beautiful Lady Raire, the unwilling companion of the dead men. Since neither Billy nor Lady Raire knows the password to re-enter the space yacht, they are effectively marooned. Eventually they find the wreck of an ancient starship and use its components to signal for help. Unfortunately, their signal attracts a ship full of hostile aliens who severely wound Billy. The aliens kidnap Lady Raire, leave Billy for dead, and depart in their ship.
Billy is nursed back to health by a giant tabby cat descended from pets that survived the starship crash. A friendlier bunch of aliens arrive on Gar 28 and give Billy a ride to another planet, where he begins his quest to find and rescue Lady Raire. After mastering the technical skills needed to crew a starship, he works his way across the galaxy, seeking the lady's homeworld. His adventures include being captured on an espionage mission, which forces him to give up his right eye to ransom the lives of his fellow spies. He endures betrayal and slavery before he finally escapes, takes revenge on his enemies, and flies off with Lady Raire.
As for the second part of your question, the story about a "fake world" could be the novelette "A Trip to the City", originally published under the title "It Could Be Anything" in Amazing Stories, January 1963, available at the Internet Archive. Here are a couple of excerpts from the story:
He went along to a door. It was solid, painted shut. The next door looked easier. He wrenched at the tarnished brass knob, then stepped back and kicked the door. With a hollow sound the door fell inward, taking with it the jamb. Brett stood staring at the gaping opening. A fragment of masonry dropped with a dry clink. Brett stepped through the breach in the grey facade. The black pool at the bottom of the pit winked a flicker of light back at him in the deep gloom.
"It's what I've been trying to tell you. This city you live in — it's a hollow shell. There's nothing inside. None of it's real. Only you . . . and me. There was
another man: Dhuva. I was in a cafe with him. A gel came. He tried to run. It caught him. Now he's . . . down there."