If object thrown vertically on moon will it travel farther than one thrown on earth?

Yes, because there is less gravity on the moon.

Also, because there is no air friction on the Moon.

However, a frisbee thrown on the Moon will not travel as far as one properly thrown on Earth, because the shape of the frisbee generates lift which will keep it flying farther. With no air on the Moon, a frisbee cannot "fly".