distances - When we say a galaxy is 200 million light years away, does this account for the expansion of space in the time it took it's light to reach us?

Usually the distance data doesn't take the expansion of the universe fully into account. That's not important for a distance of 200 million lightyears, but as we get close to the border of the visible universe, it makes a relevant difference. Therefore astronomers prefer to talk of redshift instead of distance.

To be a little more precise: The light travelling from a galaxy to Earth takes only that part of the expansion of the space between the galaxy and the Earth into account, which it still has to traverse.

For a proper distance measurement in the everyday's sense, we would have to send light to the galaxy and reflect it back to Earth, measure the time, divide it by the speed of light, and take the half of the resulting distance.

If this experiment would be performed, some of the now visible objects would never reflect light back to Earth, because they are already too far away.

For a more detailed discussion about the various notions of distance, read Wikipedia's article on distance measures in cosmology.
The usual distance data is provided in the (one-way) light travel distance.