Difference between protein channels, protein carriers and protein pumps?
No, carriers are not the same as pumps. Carriers may or may not carry out active transport and pumps always use energy. Carriers, for example, can make use of the concentration gradient of a certain ion built up by pumps to transport other molecules actively against their gradient. For example, the glucose transporter uses the sodium gradient to transport glucose against the concentration gradient into the cell, while getting the energy by co-transporting sodium into the cell along the gradient. The sodium import yields energy. That in turn is caused by the Na+ K+-ATPase, which builds up the sodium gradient using ATP. The glucose transporter is called a symporter, because it co-transports sodium into the cell. An antiporter transports another particle in the opposite direction.
Yes, true. The glucose transporter as explained above is an example of active carrier-mediated transport. Other carriers just mediate passive diffusion of, for example, large molecules that don't fit through channels and won't readily cross the cell membrane.
Yes, pumps always use energy under physiological conditions. The energy source is always ATP. 


Will add references shortly.