Your fertile window includes the day you ovulate and the preceding five days. So, for example, if day 1 is the first day of your period and day 28 is the day before you expect your next period, you'd be fertile on days 10 through 15. (But you're much more likely to get pregnant during the final three days of this window.)
Your body will recover much of the psychological craving, that is, it will stop doing the cravings by 1 to 2 months after you have quit, and then it will be time to taper the pill and the patch.
If you are getting nicotine from smoking a cigarette, you know that nicotine works quickly, so it does not last long in the bloodstream. Most of the nicotine is gone in a couple of hours, which is why most people need to smoke throughout the day to keep the nicotine levels up. It would pretty much be out of your system in 24-48 hours. One thing to note is that their are some rare people who do metabolize nicotine slowly, so just be aware that it can occur. The major breakdown product of nicotine is cotinine, which can be detected in urine. This byproduct lasts longer than nicotine, and can be found for up to one week after quiting smoking.