Do you think that's why it's going so slow
Tilt the seat forward, push the gas pedal and look at the carb. Watch the cable connected to the carb and see how much it moves with opening up the carb butterfly.
As for what make is the cart. It's a Yamaha golf cart and early G series. Same rearend from a G2 thru G14 I believe.
Your cart should have 2 cables. One from the pedal to the gov. And one from the gov to the carb. By the looks of your pic, someone may have disconnected the pedal to gov cable from the gov and connected that cable directly to the carb.
Your pic. This is the governor where the 2 cable connect. I'll see if I can get you a better pic.