You should wait until the tank is actually cycled which means your ammonia/nitrites read 0. This being said you need to add ammonia to the tank in some way so the bacteria can feed on something. Some people just add some fish flake, other does chemical ammonia to 3-4ppm. You can speed the process up by heating the tank to above 80 degrees with your heater. You can also add something like seachem stability to seed some bacteria. People have varying results on how much this speeds up the process.
The brown/green water is probably from tannins leeching from the wood. Something like purigen will help remove the tannins while not removing the ammonia from the water. In the future, the best way to limit tannins going into the water is to soak the wood for a several days in water, boil it for a few hours if you have a pot that can fit it.