I think you are better off using multi phrase queries than fuzzy query for your scenario. Fuzzy query can get very heavy and it is going to create multi terms within edit distance you have configured. From your example, it looks like all you need is an extrapolation of search terms.
Onto your second point, which search term is generated, it will be used to do a search and generate a relevance score. Finally all results will be (by default) sorted by relevance and returned back to you. I'm not sure if the sorting you are expecting will be of much value to you.