Suzuki dt25c 3 cylinder fuel pump question and idle issues

I purchased this motor from a friend not running. I cleaned the carbs and rebuilt the fuel pump. One thing I noticed on the fuel pump is that there is a spring and round plate that is pushing against the diaphragm. When I look at the parts diagram, these parts are shown, but they don't appear to be in the fuel pump. Does anyone recall ever rebuilding one of these? Do those parts belong? The original pump had them in it. Next, the motor does not idle well. It will run for a bit, then sneeze and cough out. I messed with the idle screws a little, but no luck. Any help would be appreciated. Thanks.