Is it safe to use cpap machine while I have bronchitis and a lung infection?

Yes. Just make sure that you clean the components and disinfect with something like white vinegar. Generally it is recommended to continue CPAP use unless you are having uncontrollable cough or vomiting making it more dangerous to use machine than to go without. Talk to your doctor if you are concerned.
Yes. Yes. Should be no problem unless coughing make is impossible to use. Keep machine clean. If you are experiencing problems during this period, consult with your sleep doc.