Manual electric trimming rate is fast with any flap extended and slow with flaps up.
Go around is initiated by calling "go around, flap 15" whether at flaps 30 or 40. You're correct that the normal cleaning up sequence is 30/40 - 15 - 5 - Up.
In terms of trim change it's hard to say because a lot of other things are going on at the same time; probably thrust change, increasing speed, speed trim system and levelling off. I'd summarise by saying that no flap changes have an immediate and large pitch effect but the effects are masked by drag/profile changes anyway.