3 Handle Shower Cold Water Turns On Shower
I would say that the white seal looks like it fits to the flat sealing surface at the coarse threads. The coarse threads pull the flat sealing surface onto the valve body and the white "washer" makes the seal. If this is how it works you will not need any Teflon tape or pipe dope on those threads.

I suppose the brass ring is a "valve seat" that goes into the valve body, but it has been a long time since I messed with one of these diverters and I don't know the details. Look into the hole with a light and see if there is a replaceable seat inside. Examine the edge of the seat to see if there are grooves. If you don't have a seat wrench. perhaps you should leave the existing one in place and see if the diverter works with the old one.