Despite oft printed warnings to the otherwise, you can just cut up the patches to customize the dose.

Duration of release? I believe you should leave it on 24/7. IIRC, it's not that nicotine improves sleep quality, but rather that nicotine withdrawal impairs sleep quality rather profoundly, and as such keeping the patch on at night allows for better sleep. I could be wrong here, though. Been a while since I've researched this.