Is Starman/Roadster in any danger of asteroid belt?
The Asteroid belt does contain lots of asteroids. But this is deep space. These things are not close together in any sense.
Think of it this way: If Starman had been set adrift on the Pacific Ocean, how likely would he be to collide with another ship? Pretty low? The ships on the ocean are many orders of magnitude closer together than the rocks floating around the asteroid belt.
Starman will be phenomenally lucky if he even comes within a few hundred thousand miles of an asteroid, let alone hitting one.
We've sent a number of space probes through the asteroid belt in the past, and none of them have had any trouble at all (the Dawn probe even navigated within the belt to explore Vesta and Ceres). This isn't a place like the asteroid field in Star Wars, or the Asteroids video game. There is a lot of empty space out there.
That said, we honestly don't know of all the rocks that are out there, so it is possible that Starman could encounter one of them. But it is incredibly unlikely.
You might also be interested in this question which asks about the frequency of asteroids colliding with each other.
Another relevant article on Spaceflight Now explains that the in the very long term, the likely fate of the roadster is either to fall into the sun due to orbital decay, or to be ejected from the solar system due to the influence of Jupiter.
[Edit] Final update that I'm going to make here. There's a study been done that tries to calculate the orbit and make long term predictions.
The first close encounter with the Earth will occur in 2091. The repeated encounters lead to a random walk that eventually causes close encounters with other terrestrial planets and the Sun. ... we estimate the probability of a collision with Earth and Venus over the next one million years to be 6% and 2.5%, respectively.
So yeah, general consensus is no danger from asteroids. :-)
As Simba's answer explained, the probability of a spacecraft accidentally colliding with an asteroid is very low. On average, asteroids in the Main Belt are hundreds of thousands of kilometers apart. If you could stand on an asteroid, you probably wouldn't even be able to see another asteroid with your unaided eyes. (The exception to this is when an asteroid has one or more satellites, like 87 Sylvia and its two moonlets.)
Alan Stern, the principal investigator for New Horizons, made some helpful calculations for the odds of an asteroid colliding with NH as it passed through the main belt:
Fortunately, the asteroid belt is so huge that, despite its large population of small bodies, the chance of running into one is almost vanishingly small - far less than one in one billion. That means that if you want to actually come close enough to an asteroid to make detailed studies of it, you have to aim for a specific asteroid.
Despite how they're portrayed in movies, asteroids aren't really space travel hazards. If you want to hit one, you probably have to be intentional about it.