I know that asteroids are huge chunks of rock, orbiting a solar system. Do asteroids have a gravitational field and do they gravitationally attract each other to form planets?
By definition, gravity is a result of mass. Any body with a non-zero mass (even atoms) will have a gravitational field associated with it. The higher the mass the stronger will be the field. This is basic of classical mechanics. Until we reach quantum scale where the gravitational force is dominated by other 3 forces and the gravitational field becomes irrelevent.
When it comes to graitational field of asteroids, it exists, but is very weak. However over a course of few million years these small asteroids combine together to form large masses of bodies that we now call planets. That is one of the prominent theory of Solar system formation, where the gravity of small dust particles from first our generation disintegrated star over a course of time accumulated to give us what we now know as our Solar system. Think of it like this, every planet that you see now would once have been an asteroid at some point during its evolution.
Another proof to support this is the presence of numerous binary asteroids that orbit each other around a common center of mass, which requires gravitational attraction.
Sure. Any mass has its gravitational field. However, its size is proportional to the mass, so as most asteroids have little mass, they have little gravitational field, and therefore pull only very slightly at each other, resulting in not enough effect to get them to lump together.
Typically, their difference in momentum/speed is too large to be removed by the little pull of the gravitation between them.
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.
Certainly! Anything that you see around you that has mass, your dog, your house, your car or yourself, they all have gravitational field and they exert gravitational pull to everything around them. And everything around them exerts that gravitational pull back. This pull however is so weak, that we can't perceive it with our senses. Gravity is a direct result of mass and the bigger the mass that an object has, the bigger its gravitational pull.
You can extrapolate this paradigm to everything that exists in space! From the smallest particles of dusts and comets to the biggest of stars and galaxies. An asteroid that crashes on a planet, is attracted by the planet's gravitational pull but at the same time, the asteroid attracts the planet. Eventually, this is how planets get to grow.
All celestial bodies in our sky would not exist if they hadn't any gravitational field. (1) Small dust particles collide with each other, forming bigger rocks. (2) Bigger rocks collide further to each other (or if they are big enough -several dozen of meters- might attract each other) to form comets and asteroids. (3) Comets and asteroids on their turn, will coalesce with other asteroids and rocks and will form dwarf planets and other terrestrial planets. (4) If those planets gain more mass they will be able to attract gas and they will form gas giants. (5) And if gas giants gain even more mass they will turn into smaller or bigger stars.