Are Formic queens the only fertile females?

Question

We know that Formics supposed to be similar to our ants, which have only one fertile female - the queen - that is a mother to the whole swarm. Is the same true to the Formics as well? I remember that there was a scene in (I believe) the "Xenocide" where Ender witnesses queen laying eggs of young queens inside worker's body.

But then on the other hand, I faintly remember passage from the "Ender's game" where Wiggin walks on the destroyed playground for young Formics and mentions something about "understanding, that they just like us like to watch their children playing".

Answer 1

The playground that Ender found was something that was made exclusively for him, to recreate the scene from the Fantasy Game.

I believe that your question may be concerning the following passage from Ender's Game (Chapter 15):

And from the slings that once were used to carry infants along with adults into the fields, he learned that even though the buggers were not much for individuality, they did love their children.

Over here, children doesn't necessarily refer to them as individuals (a parent caring for it's young), but rather as a species (the older caring for the younger).

Answer 2

The Buggers/Formics are basically ants, at least in certain respects. Each hive contains a single fertile female, an army of infertile females (who function as workers and warriors) and a few fertile males who exist solely to service the Hive Queen. While there are, in fact a very few queens born in each generation, the Hive Queen makes certain that they are of one mind regarding acting in a spirit of cooperation between themselves:

He walked to the mirror, lifted, pulled away. Nothing jumped from the space behind it. Instead, in a hollowed-out place, there was a white ball of silk with a few frayed strands sticking out here and there. An egg? No. The pupa of a queen bugger, already fertilized by the larval males, ready, out of her own body, to hatch a hundred thousand buggers, including a few queens and males. Ender could see the slug-like males clinging to the walls of a dark tunnel, and the large adults carrying the infant queen to the mating room; each male in turn penetrated the larval queen, shuddered in ecstasy, and died, dropping to the tunnel floor and shriveling. Then the new queen was laid before the old, a magnificent creature clad in soft and shimmering wings, which had long since lost the power of flight but still contained the power of majesty. The old queen kissed her to sleep with the gentle poison in her lips, then wrapped her in threads from her belly, and commanded her to become herself, to become a new city, a new world, to give birth to many queens and many worlds. _{^{Ender's Game}}

The scene you've mentioned in Xenocide relates to the way that a new queen is birthed. Basically the old Queen takes a worker and feeds it to the new queen at the larval stage. This then psychically bonds the new Queen to her workers and vice versa:

For a moment Valentine was simply surprised to hear Plikt's voice. Then she realized what Plikt was saying, and she was right. If a living worker had to be sacrificed for every bugger that hatched, it would be impossible for the population to increase. In fact, it would have been impossible for this hive to exist in the first place, since the Hive Queen had to give life to her first eggs without the benefit of any legless workers to feed them.

< Only a new queen. >

It came into Valentine's mind as if it were her own idea. The Hive Queen only had to place a living worker's body into the egg casing when the egg was supposed to grow into a new Hive Queen. But this wasn't Valentine's own idea; it felt too certain for that. There was no way she could know this information, and yet the idea came clearly, unquestionably, all at once. As Valentine had always imagined that ancient prophets and mystics heard the voice of God. _^Xenocide