Are you sure both of those stories were in the same anthology?
Story #1 sounds like "Interloper", a novelette by Poul Anderson, which was also my (unaccepted) answer to this old question; it was first published in The Magazine of Fantasy and Science Fiction, April 1951, available at the Internet Archive. "Interloper" is the first story in the 1951 hardcover anthology The Outer Reaches edited by August Derleth, which also includes Fritz Leiber's short story "The Ship Sails at Midnight". However, none of the stories in The Outer Reaches resembles your description of Story #2, nor does the ISFDB know of any anthology containing both "The Interloper" and Gardner Dozois's novelette "A Kingdom by the Sea" which FuzzyBoots identified as your Story #2.
Beoric, the hero of "Interloper", is an actual elf, not an "elf like alien", and it is iron that is deadly to his race, they have no problem with other metals such as copper. The enemies he is infiltrating are space aliens of various species who are the secret rulers of Earth. The aliens don't know about elves, and Beoric is passing himself off as a new kind of space alien.
They came through the line of trees onto a paved highway. A native automobile was parked there—four-wheeled, enclosed, obviously chemical-powered. As he neared it Beoric felt the sudden nerve-chill that meant—iron.
He had expected it, but that made it none the easier. Every ingrained instinct screamed at him to come no closer. Iron, iron, iron—touch it and see your hand go up in smoke! Iron, cold iron, crouched there under the moon!
And he must enter that metal box, and not for an instant must he show the fear that ripped along his shrinking nerves and dinned in his brain. If they knew, if they found the fatal weakness of the Alfar, he was done. A thousand years of slow work and scheming and waiting were done—Earth was done. It all depended on him.
For a moment he couldn't do it. In spite of his resolve, in spite of his many rehearsals, in spite of the bleak fact that he must go through with it—he couldn't. He couldn't deny the reflexes that knotted his will and brought sweat cold and bitter out on his body.
Courage. The thought quivered deep in his brain. It came from the sea, from the fields beyond the road, from the trees that stood whispering in the night wind. Courage, Beoric. You are not alone.
They were sending him more than unspoken words. There was an actual flow of nervous energy into his body, an almost physical force suddenly entering him, bracing him, stilling the wild thunder of his heart and the panic-storm in his brain. Calmness came, and he walked boldly forward.