Yes, but not directly into the lungs as mammals do (except
for some tropical fish). (Actually they breathe oxygen not air.)
As water passes over a system of extremely
fine gill membranes, fish absorb the water's oxygen content. Gills
contain a network of fine blood vessels (capillaries) that take up the
oxygen and diffuse it through the membranes.
Primarily by contracting bands of muscles in sequence on
alternate sides of the body so that the tail is whipped very rapidly
from side to side in a sculling motion. Vertical fins are used mainly
for stabilization. Paired pectoral and pelvic fins are used primarily
for stability when a fish hovers, but sometimes may be used to aid
rapid forward motion.
Tunas and tuna-like fish, billfish, and certain
sharks are the speed champions, reaching 50 miles per hour in short
bursts. Sustained swimming speeds generally range from about 5 to 10
miles per hour among strong swimmers.
Most do. The sea horse is among the exceptions.
Another is the shrimp fish of the Indian Ocean, which congregates in
schools of several individuals and swims vertically, its long tube-like
snout pointing directly upward. A catfish indigenous to the Nile and
other African rivers also swims in the vertical posture. Many kinds of
midwater deepsea fishes swim or rest vertically.
Not in the human manner. Carnivorous fish like sharks use their sharp
teeth to seize and hold prey while swallowing it whole or in large
pieces. Bottom dwellers such as rays are equipped with large flat
teeth that crush the shellfish they consume. Herbivorous fish (grazers)
often lack jaw teeth, but have tooth-like grinding mills in their
throats, called pharyngeal teeth. Fish would suffocate if they tried
to chew, for chewing would interfere with the passage of water over the
gills, necessary for obtaining oxygen.
Tuna image courtesy of "Regulatory Fish Encyclopedia, Office of Seafood and
Office of Regulatory Affairs, Food and Drug