With trees and shrubs, you really just want them to settle in and root out before they grow, so we suggest either using a root stimulator or waiting a season before fertilizing. Perennials and summer bulbs profit from a light application of fertilizer mixed into the soil as they are planted and again a month later. To be more accurate, they should probably be called shrub peonies, not tree. They bloom like other peonies and should be planted where they will have well-drained soil high in organic matter. They also like lots of sun and a site protected from winds.
Tree peonies are relatively slow to establish.
That depends on what type of soil you used last year. Pick up a handful and squeeze it. If it springs back, go ahead and use it again. Having good soil in containers makes a tremendous difference. Soil needs to hold air, water and nutrients as well as support the root systems of the plants.