I'm by no means an expert, but I will do my best to answer your questions with what knowledge I do have on the topic.
Marek's disease is a nasty viral disease that leaves the sufferers as carriers. Typically, it causes tumor growth and paralysis of the legs and sometimes wings. Less often, you hear of things like ocular deformity.
It cannot be cured and transfers from bird to bird via dander, which can be picked up at shows, feed stores, and swap meets if infected birds are present. This is why biosecurity is important--don't wear the same clothes from any of these places around your birds! It does not transmit from mother hen to egg, so hatching eggs from Marek's positive flocks are safe.
There are vaccines, but they really only work if given to the birds
within the first 48 hours or so after hatching. The vaccine does
not cause the disease and will
not make vaccinated birds carriers,
but if they come into contact later on with Marek's disease they will become asymptomatic carriers. This means they will carry and pass on the disease, but not show any symptoms of it.
It is contagious only to birds, and I believe it only affects chickens under normal conditions.
It does not transfer from bird to mammal in any way. You and your critters are safe from infection.
This is an awesome article about Marek's and it's written in a way that's pretty easy to understand. Check it out if you want to know more:
https://www.backyardchickens.com/a/the-great-big-giant-mareks-disease-faq