The second derivates in this case refer to how quickly the price is changing. If the second derivative is (+), then the instantaneous price is rising. If negative, it's falling. If zero, then the revenue change is unchanging. If this seems complicated, take calculus, it's fairly intuitive.

The second question is fairly ambiguous, so I'd say it's a trick question and go with no. If the quantity is decreasing, you'd expect the price to rise. This is also basic econ.