"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.

"What connections come at the both ends of your grease trap interceptors?"
Both ends come with no-hub fittings. In other words, they come with a plain end. To adapt the ends to steel or plastic pipe you simply use a standard no-hub adapter.