There really aren't many illnesses that cross between cats and humans, but you should always wash your hands after handling animals. Avoid changing the litter box or touching any vomit or feces. If nobody else can clean those up for you, wear gloves and wash your hands VERY thoroughly with soap and warm water.
Its not very common for an animal virus to transfer to a human but that doesn't mean it cant. Just make sure to thoroughly wash your hands after you take care of the cat just to be safe!
Be careful, cat feces can contain harmful bacteria that can affect the baby it's called taxoplasmosis and is found in cat feces. Have someone else change the litter bix and if you absolutely have to do it try wearing a mask over your mouth and nose
I doubt it. But I don't know for sure but a lot of viruses can transfer from species like thay