1. Can the numbers in a geometric sequence go down?

Yes, if the common ratio is a fraction the terms will decrease.

2. What happens in a geometric sequence when the common ratio is negative?

Each term will change sign, that is the sequence will oscillate.

e.g. A sequence with first term of 3 and a common ratio of -2 will be 3, -6, 12, -24, 48, ...

3. Does the common ratio have to be the same between every pair of terms for a sequence to be an geometric sequence?