In my opinion, there is no clear answer to these questions in the book.
In Ch. 23, it is stated that the Overlords could not explain why there are no more children, although Jan suspects the lack of new births was due to psychological reasons.
There had been men on Earth as little as ten years ago, but they had been degenerate survivors and Jan had lost nothing by missing them. For reasons which the Overlords could not explain, but which Jan suspected were largely psychological, there had been no children to replace those who had gone.
So, the Overlords said there are no new children, but it is not stated if these children would be "evolved" or not. We can only speculate that they would be, since this "evolution of mind" happened to many people simultaneously. From the end of Chapter 19:
Jeff and Jenny had been the first in all the world, but soon they were no longer alone. Like an epidemic spreading swiftly from land to land, the metamorphosis infected the entire human race. It touched practically no-one above the age of ten, and practically no-one below that age escaped.
About the second question: although, again the book is not 100% clear, since all other humans died before
It does not seems that Jan, at least, would be disallowed to go with the Overlords - he choose to stay on Earth voluntarily, and Rashaverak questioned him if he is sure about his choice, so it is hinted that he could choose to leave Earth. From Chapter 24:
JAN: "I shall stay, " said Jan abruptly . "I have seen enough of the universe . There's only one thing I'm curious about now- and that is the fate of my own planet. "
Very gently, the ground trembled underfoot .
JAN: "If, of course, the Earth still exists."
RASHAVERAK: "You realize that danger-and yet you will stay?"
JAN: "Yes. I have been home five-or is it six?-years now. Whatever happens, I'll have no complaints."
RASHAVERAK: "We were hoping, " began Rashaverak slowly, "that you would wish to stay. There is something that you can do for us .