Regarding your sleepiness and lower nic content; Yes, you will feel more sleepy and/or sleep more when reducing the nicotine intake you are used to. I've tried quitting smoking 3 times before, and have used the patch all
three times. I noticed that I was sleeping more, and was more sleepy/groggy during the day. This is a natural reaction to withdrawal symptoms.
As you reduce the intake of nicotine, your brain must produce the chemicals naturally that the nicotine helped to stimulate. The ending result is a feeling of either restlessness (can't sleep/light sleep/bizarre dreams) or that of utter crashing (sleeping 12-14 hours, taking frequent naps, feeling groggy or unfocused).
These symptoms will go away in time, and during my 5 months of smoke-free living, I noticed that my sleep pattern changed dramatically
throughout a matter of a couple months. By month 4 I was sleeping about 7 hours a night, and felt rather normal, aside from the depression I realized I was experiencing (which, by the way, is why I started smoking again).
Hope that helps.