when you tamp down to keep your pipe lit, should you be taking in puffs while doing so?
The first tamp is after filling the bowl, prior to the charring light, done with the index finger so the tobacco feels "springy" and not tightly packed in there.
The next tamp (with your tamper this time) is after the charring light (when you're doing the charring light, you do puff, so as to get the tobacco lit). It's not uncommon for the burn to quit while you tamp -- you're leveling out the charred tobacco in preparation for the true light.
The true light is next, here you light the tobacco evenly and puff while doing so. If you've dried out the tobacco properly, it should stay lit, but if it does go out anyway (it does happen), tamp lightly but evenly and perform a re-light.
while I have the pipe in my mouth and breathe, some air tends to go back into the pipe. Is this something that is killing my burn?
No. You might get embers and ash in your face and on your clothes if you breathe out too hard, so try to avoid doing that, but a light breath back into the pipe won't kill the burn.
with lighting, how long should I keep the flame over the tobacco?
First use a match (best), or a lighter such as a Zippo for pipes (good), or a soft flame butane (OK, but be careful), and *never* use a torch. The reason for this is butane can be too hot and torch lighters, while fine for cigars, can burn the crap out of your pipe's wood. Keep up the true light process, puffing, until the tobacco is evenly lit.
I hope this helps you out