1960s anthology; one story was about people living in cocoons but still looking for one where female scientist is seduced by the plant king

Question

In the 1960s, I read two short stories in a sci-fi paperback anthology magazine. I would like to know the anthology that they were in (and the titles of the two stories, obviously)

1. Future age on Earth (I think) where people exist in cocoons and only talk with and see other people as icons. One man realizes something is wrong, sees transmissions from actual people saying there is a new ice age and warning that everyone is going to die if they don't leave their cocoons and escape. He has to disconnect from the apparatus and live in the real world. [This one has been identified; it is "Cocoon" by Keith Laumer.]

2. Woman scientist on another planet explores the forest and is seduced by the plant king. She sees a green man peering at her from the trees. He woos her and she falls for him. She gets pregnant. The other humans are upset, then when she gives birth to a new species by sort of unzipping like a pea pod, they are in awe and fear. The child(ren) is a hybrid. She's declared a queen, I think, and I vaguely remember them being worshipped. The overall feeling is mysterious and green and almost an origin of species kind of story. Very weird and haunting story. [It's NOT Keith Laumer's "Hybrid".]

Answer 1

The first short story is "Cocoon" by Keith Laumer, which was also the answer to this question. It was first published in Fantastic Stories of Imagination, December 1962, available at the Internet Archive.

An excerpt from "Cocoon":

A face appeared. This was a different one, Sid was sure. It was hairier than the other one, but not as hollow-cheeked. He watched in dumb shock as the mouth opened—

"Listen," a hoarse voice said. Everybody, listen. We're blanketing all the channels this time—I hope. This is our last try. There's only a few of us. It wasn't easy getting into here—and there's no time left. We've got to move fast."

The voice stopped as the man on the screen breathed hoarsely, swallowed. Then he went on:

"It's the ice; it's moving down on us, fast, a god-awful big glacier. The walls can't stand much longer. It'll either wipe the city off the map or bury it. Either way, anybody that stays is done for.

"Listen; it won't be easy, but you've got to try. Don't try to go down. You can't get out below because of the drifts. Go up, onto the roofs. It's your only chance—you must go up."

The image on Sid's contact screens trembled violently, then blanked. Moments later, Sid felt a tremor—worse, this time. His cocoon seemed to pull at him. For a moment he was aware of the drag of a hundred tiny contacts grafted to the skin, a hundred tiny conductors penetrating to nerve conduits—