Hi, you can use "cannot" or "can't" to describe all three of these situations.
"Can" and "can't" have many different meanings. These include:
1. permission ("Can I go to the movies tonight, Dad?" "No, you can't.")
2. ability ("Can you speak French?" "Yes, I can. Bonjour!")
3. possibility ("What can you do for fun in New York?" "You can go shopping, you can go to a museum, or you can go to Central Park.")
Also, "can't" means something is logically impossible.
"She can't be sick. She's dancing!"
BUT you cannot use "can" in this way.
"Jane didn't come to work today. She MIGHT / MAY be sick." (NOT "can")
I hope this helps! There is a lot to learn about words such as can, should, may, might, would, etc.