The 1 / focal length guide applies to 35mm equivalent focal length, so for crop sensor it does get that bit worse.
Why would that be true? Not questioning your personal experience but what's the technical reason for that. Possibly because with a crop-body you're standing further away for the same framing, so the angle of view is less, and vibrations due to hand shake would then cross a greater angle. Ok, true assuming same framing which is the case 99% of the time.
It's roughly true in my experience but not specifically due to it being a cropped sensor (as far as I can tell), more that cropped sensors see higher pixel densities (a 5d2 would be about 8mp as a crop with the same density but a 7d would be around 45-47mp as a full frame). In digital medium format, as sensors mp counts have increased drastically that requirement for better technique to avoid blur has increased along with it. I find with the same 50mm lense I need 1/60 on the 5d2 but 1/90 on a 7d for a high keeper rate, However 1/60 is about right for my 50mm on my rz67. If 1/fl holds true on a 6x7 like it does on 35mm it should also hold true for apsc. I guess if canon made a 45mp full frame sensor (sony probably have a 45mp apsc in the works ;-) ) it would probably need better technique or a faster shutter speed. By 'better technique' I refer to methods such as a tripod, IS, holding breath etc, I'm being clumsy with the wording, been awake too long, I mean just taking steps to avoid operator induced blur.
I found (as many did) the 7d to be more demanding than the 10d, 20d or 40d in that respect.