I will try to answer your questions as best as I can, as I myself am learning.
1.)What are the rules of morality?
The rules of morality are pretty much what influenced all the Abrahamic faiths. The concept of good vs evil, light vs dark originated largely from Zoroastrianim. The main aspect of our faith is Good Thoughts, Good Words, Good Deeds and to practice all three as much as we can.
Basically the whole religion is built around the notion that God and Evil are separate and have always existed. As such our whole existence revolves around fighting evil and chaos by doing good. Each one of us is responsible for doing good in the world and it is a part of our own individual imperative to promote good and limit evil, pain and suffering. Although Ahura Mazda is extremely powerful, we need to do good to prevent Ahriman, or the evil entity in the universe to prevail.
There is a lot of importance placed on the actions of the individual. To me this has satisfied my own explanation for evil, while the Abrahamic faiths think of evil as either some sort of mistake in God's creation or the fact that God created evil to 'test' us, I think the concept of evil as a separate entity makes more sense.
2.) Is there an afterlife?
The concept of heaven and hell are also Zoroastrian concepts. The word Paradise is from the Zoroastrian word Parizadea. When we die we are meant to cross a bridge where we are judged for our sins.
However one major distinction between the Abrahamic versions of heaven and hell and the Zoroastrian ones is that the joys and punishments are mental, rather than actual things. In hell there is no fire or brimstone, but negative energies and thoughts. Hell isn't eternal either.
Eventually there will be a Messiah or a Sayoshant who will resurrect the dead.
3.) Is there any kind of dress code in the way that some religions promote modesty?
In public not really it depends on the culture, in place of worship the women cover their heads and dress modestly, with skirts below the knees and nothing too revealing. The men are supposed to wear pants and cover their heads when we pray as well with a cap that's similar in size to what muslims wear. We have to cover our heads when we pray.
4.) What might be a good book to get started in learning more? Since in the Southern parts of the US I only heard of Zoroastrians in religious studies class.
There are several sites on the internet which are good. I would suggest you stay away from a lot of Parsi material as it's filled with ethnic issues and superstition and try to stick more to Iranian and other sources written by Parsis in the West who have distanced themselves from the Indian views.
Here's a good site I like to visit and read:
CONVERSION IN ZOROASTRIANISM; The Truth Behind the Trumpery - (The Circle of Ancient Iranian Studies - CAIS)©
If you live in the South I don't know much, since I live in the North. The biggest communities in North America are in Toronto and California. I think Texas might have a few as well.