How to connect microphone to guitar pedal to pa?

Here's the issue. Your mic is a low impedance device and the DD3 has a high impedance input. It's not just the fact that one is 1/4" and one is XLR. The device in your link should do the trick. For the output from the DD3 to the board you can go out of the DD3 to a high impedance input on the mixing board or use a direct box on the output side of the DD3 to convert it to low impedance and take that to a low impedance (XLR) connection on the mixing board. Some mixing boards also have an effects loop so that you can plug the DD3 directly into the mixing board and then just apply that effect to the channel the vocals are on.