the tank its self. it can feel frozen. but wont break when dropped. if you mean the oxygen its self. . . yes oxygen can freeze. all elements have a freeezing point. Oxygen has a freezing point of -368.77 °F.
Yes it could but the temperature would have to be really super low for that to happen, as oxygen has a freezing point of -361.82 degrees Fahrenheit.
Yes of course if the tank is not properly vacuum insulated.