Just thought of something - what kind of relay do you have? Can you post a link? I use one of those little relay modules you can get cheaply on ebay. But some of them are set up so that they trigger when the pin is set to LOW instead of HIGH. If it's clicking for the initialization, that may be the reason.
For the debug: I just checked this. Using Programming Editor 6 (I can't get 5 to work on my computer any more, it can't see the adapter since I went to Windows 10), make sure you have the Code Explorer window visible on the right, and that the Debug button is clicked. After programming the Picaxe, you will see "Debug - Waiting for Data..." in the very lower-right corner of the Programming Editor. This will stay there until the warmup cycle is done - the LED will stop blinking. Then it will change to "Debug Active".
Then look at the top of the Code Explorer window, you will see two variables being tracked, PIRWarmup and TIMER:
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As you pass your hand in front of the PIR, you should see TIMER change from 0 to 5, and then the LED will blink. Then there's a Reset time before it can be triggered again. You may need to make this longer depending on the prop and the PIR. Sometimes the PIR will need more than five seconds to "cool down", change that in the ResetTime variable at the top of the program.
That should get you started, once you have it going then you can describe in more detail what the prop is and how you want it to behave.