Likeliness is a VERY uncommon form of likelihood. I believe the two are interchangeable, but I have NEVER heard anybody use the word likeliness. Likelihood deals mainly with the probability that something is going to happen. Possibility deals more with the feasibility, in other words, if something is possible. I'll try to explain what I mean by using a couple examples. If you drive a car there is always the possibility that you might die in a car crash. However, if you drive a car and crash at a high speed while not wearing a seat belt the likelihood that you'll die is great. I hope that helps.

2. My coach says that a helmet lessens the likelihood of injury.

As a native English speaker, I have to disagree that likeliness is uncommon.... it is extremely common. In fact, I probably hear that word used more frequently than likelihood.