My fiancée is going to university, working towards a degree in dentistry. For about a year, she will be required to handle cadavers in the classes. First of all, is this forbidden in Torah? Secondly, what sorts of purification will be required? Is it considered like niddah (i.e, will I be prohibited from marital intimacy?) I appreciate your answers on this. We are both new to Torah.
you've come to the right place.
More on the subject here, but in short:
If someone is a [male] Kohen, they're prohibited from any additional contact with the dead -- thus it's problematic for a Kohen to handle cadavers. (If you have no particular reason to believe someone is a Kohen, we generally don't worry about it.)
Other than that, today we're not usually concerned with the laws of ritual purity. Someone could be an undertaker or mortician and touch dead bodies all day long, that's fine. That means they can't enter the Temple or eat sacrifices, but that's kind of moot right now anyhow, so not to worry. Basically there's no purification today that's necessary (or even helpful -- it would require Red Heifer Ash which we don't have). Though many volunteers who prepare corpses for Jewish burial (known as chevra kadisha -- your fiance may consider joining) find it psychologically helpful to shower and put on clean clothes afterwards.
Nida is a very localized set of laws. Yes a Nida is not ritually pure, but we don't worry about that today. However, immersion is still needed specifically for the purposes of marital relations. A woman could be a mortician and touch a corpse Sunday through Friday, she'd still observe the laws of Nida -- and immersion -- like anyone else.
Judaism does believe in treating a human corpse with a certain amount of respect, which includes leaving it intact barring strong reasons otherwise. ("Strong reasons" could include harvesting corneas postmortem, or an autopsy that could help find a serial killer on the loose.) We're thus not crazy about someone donating their body just for general medical research. However, your question is on the opposite side of the table, once the body has already been donated -- non-Kohen Jews routinely enter medical and dentistry school and study on cadavers. Years ago someone asked Rabbi Joseph Soloveichik about this, and he replied: "would you trust a doctor who's never taken apart a real human body before? I wouldn't!"
It would still be appropriate to show as much respect as possible, e.g. limiting side conversation and jokes while dissecting the cadaver.