"Does a grease trap prevent blockages and stoppages?"
Grease traps do help prevent stoppages after the trap but blockages can (and do) occur as a result of insufficient (not frequent enough) grease trap line maintenance. A grease trap or drain line which is not periodically maintained (you must take the grease out of the trap) will eventually clog.

"Why does my grease trap back up and overflow? If I buy a new one from you will it backup and clog less?"
Grease traps back up either because they need to be cleaned or because of an outlet blockage. Buying a large unit would mean you'll need to clean it less often as there is more storage capacity of grease. But please understand that all grease traps will clog if you don't clean the grease regularly.

"How does a grease trap work?"
A grease trap works by slowing down the flow of warm/hot greasy water and allowing it to cool. As the water cools, the grease and oil separate and float to the top of the grease trap. The cooler water (less grease) continues to flow down the pipe to the sewer. The grease is actually trapped by baffles, which cover the inlet and outlet of the tank, preventing grease from flowing out of the trap.

"Yesterday I had our grease trap pumped clean and today the trap overflowed. Why did this happen?"
Hopefully you had it pumped before it was stopped up. Pumping the grease trap alone does not prevent stoppages down the line. While pumping grease, grease can get into your main line if the pumping is done wrong. Also, if you had it pumped because you had a stoppage and so assumed it was due to the grease trap, it might be that you had a partial stoppage already in your main line.

"My local governmental code wants to know how long the water stays in the grease trap?"
Basically the way some (many operate differently) health/safety/engineering departments figure the grease trap size needed is that they wish for you to keep the water in the trap for a certain period (length) of time. What that means is that if you have a 3 gallon per minute drain flow, and a 30 gallon grease trap, some agencies will consider the 3 gallons as having a 10 minute "hold" time. You figure this by dividing the gpm by the gallon volume of the trap.
Not all governmental bodies operate the same way and so, please, contact them before you order a grease trap. Make certain that the size that you are ordering is the size that they will accept. Note that all grease traps have a maximum flow rate. Also note that for sanitation reasons, (all brands) grease traps are sealed and not open to the elements. Some brands of grease traps are difficult to open (not ours) but, in all cases, all grease traps are sealed. Again, generally (not always), the size of the grease trap versus the gallons per minute of your drainage is what determines the size that you are required to have. Please be certain of the size that is required by your local code or governmental regulatory agency because shipping is very expensive and we do not take them back.
When in doubt, do not order these until you are certain of what you need. The codes are designed to try to take the most grease out of the water. If you under size your grease trap then some of the grease could pass through and also you might need to pump out (take the grease out of) the trap quite frequently.