Certain operations are guaranteed atomic on all platforms. The first class of operations work on atomic_t include/asm/atomic.h; this contains a signed integer (at least 32 bits long), and you must use these functions to manipulate or read atomic_t variables. atomic_read() and atomic_set() get and set the counter, atomic_add(), atomic_sub(), atomic_inc(), atomic_dec(), and atomic_dec_and_test() (returns true if it was decremented to zero).
Yes. It returns true (i.e. != 0) if the atomic variable is zero.
Note that these functions are slower than normal arithmetic, and so should not be used unnecessarily. On some platforms they are much slower, like 32-bit Sparc where they use a spinlock.
The second class of atomic operations is atomic bit operations, defined in include/asm/bitops.h. These operations generally take a pointer to the bit pattern, and a bit number: 0 is the least significant bit. set_bit(), clear_bit() and change_bit() set, clear, and flip the given bit. test_and_set_bit(), test_and_clear_bit() and test_and_change_bit() do the same thing, except return true if the bit was previously set; these are particularly useful for very simple locking.
It is possible to call these operations with bit indices greater than 31. The resulting behavior is strange on big-endian platforms though so it is a good idea not to do this.