This can be cured somewhat by chewing with your mouth closed. Nervous people with fast moving bowels will fart more because less air is absorbed out of the intestines. Some disease conditions can cause excess flatulence. And going up in an airplane or other low-pressure environment can cause the gas inside you to expand and emerge as flatulence. No, a burp emerges from the stomach and has a different chemical composition from a fart.
Farts have less atmospheric gas content and more bacterial gas content than burps.
There are differences in opinion on this one. Certainly, people have believed for centuries that retaining flatulence is bad for the health. Emperor Claudius even passed a law legalizing farting at banquets out of concern for peoples' health. There was a widespread belief that a person could be poisoned or catch a disease by retaining farts. Doctors I have spoken to recently have told me that there is no particular harm in holding in farts.