some cats are smarter than others but some cats need help to spit out the furball (hairball) since they might not have enough strength to. If the cat is old you really need to keep an eye on the cat...
If you can't breathe at all, you would go unconscious around one minute (maybe a little longer if you had air in your lungs). By three minutes your brain would be damaged, and your heart would...
Depends on the situation. I would call an Ambulance at least. I teaspoon of liquid would probably not choke her though. Cough yes, but not choke. And no, it wouldn't be your fault since she chose to...