No it can't
No if you don't eat it just keep it clean and wash your hands after you play with it
Cleanliness is most important to the good health of a hamster. If you think you can catch a disease by cleaning a hamster cage, I would suggest good personal hygiene habits and wash your hands thoroughly and I don't believe you will catch anything. It is also good to know that if you think you are getting a cold, you should not be handling your hamster as you can pass these germs on to the hamster. You can potty train your hamster and clean the potty every couple of days, and scoop out the poop from around the cage with a little hamster potty shovel.
Whenever handling any pet, always wash your hands with soap and water.