gravity - Do asteroids have a gravitational field?

You asked two questions.

Do asteroids have a gravitational field.

Of course. Even a microscopic grain of dust has a gravitational field.

Do they gravitationally attract each other to form planets?

Not any more. During the formation of the solar system, asteroid-like and comet-like objects collided to build larger objects, which in turn collided to form even larger objects, and so on, eventually building the cores of giant planets and later, the terrestrial planets. But that stage ended long ago, shortly after the solar system formed.

Asteroids do of course gravitationally attract other objects, but this attraction is so weak due to the small masses of asteroids that it is easily overwhelmed by other perturbing forces. The vast majority of the asteroids lie between Mars and Jupiter, and Jupiter is the primary culprit in explaining why no planet exists in that gap.

When two astronomical bodies collide, one of the outcomes is a purely inelastic collision that makes two bodies form a single body. This only happens with a rather mild collision. A more energetic collision will result in some mass being expelled. An even more energetic collision will result in lots of mass being expelled; the colliding bodies become many smaller bodies. With a few exceptions, the latter is what is what is happening amongst the asteroids today, and for the last four-plus billion years or so.

Jupiter is such a huge perturbing body that collisions in the asteroid belt are generally very energetic. Instead of forming ever larger bodies, the asteroid belt is gradually being broken up into smaller and smaller bodies. Some of these collisional bodies are ejected from the solar system thanks to interactions with Jupiter. The smallest results of these collisions migrates sunward thanks to the Poynting-Robertson effect.