1. All the money was gone.

2. All the money disappeared.
(Are both the same?)

3. Chandra examined the elephants and found a problem with their ears.
(What is the meaning of 'with' in this sentence? On/In which part did the elephants have a problem, in their ears or on their ears outside? What other expressions can we use instead of 'with'?)

1 and 2 are fine and mean about the same thing.

3. The word "with" here is just indicating the general area where the elephants' problems are. If you mean the problem is inside the ears, then you'd use "in" instead of "with" -- and if the problem is on the outside of the ears, then you'd use "on."