A poster child is a representative example of a situation, quality, or activity. It can be: a person, a group of people or things, an organization, an object, a concept, an idea, a theory, etc.
There is very little difference in meaning between without and with no. For example, you can say "without success" or "with no success". Both expressions are correct and mean basically the same.
Pushing on a string means that your strategy, despite investing all your energy and efforts, is not working. In other words, you do not succeed in achieving your goal because what you are doing is ineffective.
The verb to avail has two basic meanings: 1.) "To avail oneself of something" means making good use of something, or taking advantage of an opportunity. 2.) "To avail" can also mean "to help" or "to be useful" (mostly used in negative sentences).