In Linux, what happens to the state of a process when it needs to read blocks from a disk? Is it blocked? If so, how is another process chosen to execute?
While waiting for read() or write() to/from a file descriptor return, the process will be put in a special kind of sleep, known as "D" or "Disk Sleep". This is special, because the process can not be killed or interrupted while in such a state. A process waiting for a return from ioctl() would also be put to sleep in this manner.
An exception to this is when a file (such as a terminal or other character device) is opened in O_NONBLOCK mode, passed when its assumed that a device (such as a modem) will need time to initialize. However, you indicated block devices in your question. Also, I have never tried an ioctl() that is likely to block on a fd opened in non blocking mode (at least not knowingly).
How another process is chosen depends entirely on the scheduler you are using, as well as what other processes might have done to modify their weights within that scheduler.
Some user space programs under certain circumstances have been known to remain in this state forever, until rebooted. These are typically grouped in with other "zombies", but the term would not be correct as they are not technically defunct.