When I was playing, every time new features were added, we had to start a new world to get those features. Does it still work that way? Say, if I was playing an old world and Mojang adds a mob that spawns on grass, will they spawn on grass in a world created before that patch?
Yes, it should work like that, any old map can have new features, so long as it's not world-related (such as biomes, because then you will need to go further out of your world), but if it's something like a mob, it will work on older maps (since they are both spawning on the same block ID).
Yay.