Frequency questions and searching for pulses...

With the Binary Pulsar search being back in the spotlight, I was thinking about this post by Benjamin : Plans for near future of E@H ?

Looking at this page E@H GRP discoveries and Einstein@Home Arecibo Binary Radio Pulsar Search (Re-)Detections

And a couple of questions about frequency searches sprang to mind.

If a simple metronomic pulsar is is tick-tick-tick-ticking at 100Hz, would it be detected at 50Hz by our searches? My simplistic logic being because it would show two perfectly formed peaks 180 degrees apart (a harmonic?), 4 peaks at 25 Hz each 90 degrees etc.

The phase diagrams on the GRP pages i find amazing, for many reasons (the meagre amount of photons being one, the visual representation being another), but they made me think about this.

Is the published frequency of the pulsar equal to its spin OR the frequency of the pulse itself?

If we see only one pole of a pulsar, we could say the rotation speed is the same as frequency, but if we see two poles edge on say, then the rotation frequency would be half that observed, as we would get two pulses per rotation.

Either way - is this problem solvable, and how?