If you do not want the seed pods to develop, cut the stalk off at its base once the flower petals have dropped. If you don't mind the seed pods, wait until after the first frost and remove the stalk...
The main reason to remove some of the bottom part of the stem is to remove air bubbles that may have entered the stem. The bubbles prevent water from being drawn up the stem, resulting in the flower...
You don't ever need to have the tail cut off, but if you wanted to, you should do it at birth.
Cutting off a dogs tail is called docking. The only occasions when it should be carried out is for...