Getting my hands around use of taxonomy terms

I was drawn to Drupal because I could see the tremendous potential of using taxonomy terms to affect the way a page looks, as well as what features might appear in it. However, I'm having trouble grasping how to make full use of this and I'm hoping someone can steer me in the right direction.

I'm familiar with the concept of parent>child, but I don't understand how to work within the hierarchy.

Let's say I have several layers of terms. For example, a term "bulldog" is a child of "dogs," which is a child of "mammals," which is a child of "animals." So we have this: animals>mammals>dogs>bulldogs.

I can conceive of several instances when I'd want to make my pages appear differently or have different blocks based on levels of that hierarchy.

For example, I might want to use a different CSS for "mammals" than what I'd use for "insects." But that CSS needs to apply to all children of "mammals" as well, such as "dogs," "cats," "pigs," etc.

And by the same token, I might want to have links to pages about dogs only appear on all pages created with different children of "dogs."

So here's where I have trouble understanding: When I create content about, say, bulldogs, do I have select the terms "animals," "mammals," "dogs," and "bulldogs," or is there a way to set it up so that if I select "bulldogs," the parent terms can be assumed? If it's a bulldog, it must be a mammal, so can the CSS for mammals be automatically used without me telling Drupal my page is also about mammals?

Related to this, let's say I've created a block that appears only on pages about dogs, but that includes the child terms of "dog."

I'd like to be able to use some kind of code (PHP?) to assign the block to all child terms. So rather than listing all terms, like "taxonomy/term/1," "taxonomy/term/2," "taxonomy/term/8," I can tell Drupal that any child of dogs will use this block. That way, if later I create a new child of "dog" I don't have to go back and add the new term to the list of assignments for the block.

I hope I'm making sense of this.

Please share your wisdom on this, because as hard as I try I can't seem to find documentation that clarifies it for me.