Under the schools a recruit is considering, is that the order in which they are considering the schools? For instance, if it lists, top to bottom, Wisconsin, Michigan, Iowa, does that mean Wisconsin is the top choice, Michigan No. 2 and Iowa No. 3?

I noticed a change in the order with a player I am battling another school for when I offered a scholarship just now.

No, there is nothing to order. You can see it change with each refresh if you want to.