Heat is a great tool
No, ClickHeat doesn't always generate 1000px high pictures. But it may :-) This is a computation between the width, the memory limit and the final memory size of the image. But AFAIR, it limits it to 1000px max, that's a point (else there would be pictures too big for nothing).
For example a 1000x1000 image is the same size in memory as a 2000x500. So it depends on the width you've selected, and the memory size you've selected.
The fact is that the maximum height isn't computed before generating images, for speed purpose. This will be fixed in the next release of ClickHeat, which will be the Piwik Heatmap Plugin (ClickHeat v2.0 will never see the light).
For the «no clicks below» issue, that's just because it's not associated with the actual height of clicks, but it's the end of the last image generated. The idea was to explain why there was nothing (no overlay/picture) below this line (because there was nothing to generate!).
Try to lower your memory limit, this will create more images, and perhaps solve your issue. Or remove the 1000px limit, setting it to 1500 for example (file Heatmap.class.php, line 107)