My doctor put me on the pill at my first follow-up visit after I had my son. I had not had my first period yet and I was also breastfeeding. Because of the breastfeeding, she prescribed something with less hormones or a different hormone or something so that it wouldn't affect my son. The pill shouldn't affect your possible pregnancy because you wouldn't be very far along. A lot of women end up drinking, smoking, and doing other hazardous things before they know they're pregnant and they usually have normal, healthy babies. So if you want to start the pill again, I'd think it would be perfectly safe as long as you stop once you find out if you're pregnant or not. If in doubt, ALWAYS call your doctor.
As for the home test, the boxes say you can test as early as 10 days after you think you conceived, but if you don't produce high levels of HCG it won't pick up on it and you'll get a false negative. I got a false negative at 6 weeks with my son and a positive at 7 weeks. So it all depends on how much HCG you produce. Good luck though! And don't worry, you're not the only one with questions about the pill. I only know this stuff because I asked my doctor.