Yes.
It depends heavily on your game settings, namely Monster evolution scaling factor
and Spawn rate scaling factor
.
This answer from an other topic explains it well:
Since you’re playing in the same world, you can run into the same (already evolved) monsters or monsters with it’s timer getting close to evolving. If you go into newly generated terrain, I’m not sure, but I think it uses the (newly) generated evolution timer of your current character.
To my understanding it wipes your world completely and just keeps the mod list. That should reset the timer for sure.
Dreams are mutation related. See the wiki pages on mutations and dreams (spoilers).
Or for short (taken from said wiki page): Once you are sufficiently mutated, you will begin receiving dreams, relating to how strongly mutated you are toward your highest category.