How fast does a tornado travel and how fast is the wind in a tornado?

Both of these values are highly variable. Tornadoes can be stationary or move at over 70 mph. A typical speed would be around 35 mph.
Most tornadoes produce winds of less than 110 mph and winds may be as low as 60 mph. However in extreme cases, winds in a small portion of an exceptionally violent tornado may exceed 300 mph.