I do have a few questions. Is the Smoking Sea where Valyria used to be before the Doom?
Well, partly. Valyria is still there, as you can see from the maps. But it wasn't always on an island.
Was the Doom related to dragons, i.e., did the Valyrians lose control of some of the dragons, or was there some sort of civil war fought with dragons much like occurred later in Westeros?
No comment.
Finally, will there be new maps in ADWD? I love the maps and would like to see where the Free Cities, Yi Ti, Asshai, and the Shadowlands lie.
Yes, there will be new maps in every volume. Which ones depends on where the story goes.
Is Yi Ti farther east than Asshai/Is there anything known to be east of the Shadowlands?
You'll need to wait and see.