I am training for mma, but have beensidelined for 2 weeks because of bronchitus, with just a bit of chestcongestion. Should I begin to train again?
Yes. The danger of training while sick is not allowing your body to rest, thereby prolonging your illness. If you are only mildly affected by your symptoms, go for it.
Not if coughing!!! Mma unlike other sports (except for wrestling) is very "in your face" as you know. I would say it's ok to start hitting the bags, doing light cardio etc, but don't start grappling until you are completely over your bronchitis. For one thing, you don't want to pass the infection to your training partners in the gym. Nothing worse than having someone pass on their infection in the gym.
Probably ok now. As long as you have no fever, shortness of breath, chest pain/tightness or significant fatigue, then you should be able to resume training again.