This is a terrific question, and the answer is we don´t know exactly. Feelings are tough things to measure. To be able to understand feelings we would almost need to be able to read peoples´ (or elephants´) minds. Actually the question of whether or not elephants have feelings is something that scientists have debated for many years. We do know that elephant are highly intelligent creatures. In fact the brain of an elephant is very similar to the brain of a human in terms of complexity.

Elephants also have a wide range of observable behaviors: elephants have behavior associated with grief, compassion, cooperation, memory, learning, playing, using tools and many more very complex behaviors. All of these things indicate that elephants are very smart animals indeed! And, in general, intellectual animals are also capable of feeling emotions and having feelings. So it´s certainly possible!

Yes, not unlike humans.