Justice and Fairness literally mean the same thing, but each word has a different feeling to it. Justice has the feeling of importance and seriousness. When people talk about Law they use the word Justice. The word Fairness is much less serious (even though it means the same thing). If you had two children and you gave one a cookie, the child would say "I didn't get a cookie, that's not fair!!". But he wouldn't say "that's not just!!!" (unless he was trying to be funny and overly dramatic)
Recognize means you see someone or something and your brain remembers that you know this person or thing. You could recognize a person, or a famous painting, for example. Acknowledge is something you do after you've recognized. An easy example is a person you meet on the street, let's say you recognize them as a person you went to school with. You Acknowledge them by waving hello and smiling. To acknowledge someone is to show them that you recognize them. But what if you didn't like this person? Then you may decide to walk right past them without saying anything. In other words, you don't acknowledge them. To recognize is an involuntary thing, your brain will either do it or it won't. To acknowledge is a choice you make on each occasion.
Acknowledge is used for ideas as well as people you meet. Before we travel to other countries we may read about their culture. When we visit them we will Recognize the things we read about, and in some cases will be forced to Acknowledge that their way of doing things is much more Just or Fair then our way of doing things back home.