I can't address the factors on skin condition, but I can tell you about the experiences between laser sessions. For me, it takes a fews days to be able to get a few hairs by tugging gently with a tweezer, but mostly, they won't come out easily until about 10 days after. So during that time I don't shave because I want the hairs to be pushed out and to see the length of them. After the hairs have fallen out, you'll be able to see the areas that have been cleared or where the new crop is ready to grow, or the ones that just didn't die.
For a while, say about the third/fourth week my face was cleared except for new hairs. Once they began to emerge, the hairs came out in random patterns/clusters. It was at this point that I would shave just to not look so weird.
I am able to get my laser done on Sundays, so on Thursdays I would let the hair grow out and take pictures of my face Sunday morning before laser to track the growth/removal patterns. Then I'd shave for the session.
It is worthwhile to track the progress, and the best time to see that is just before the next session, that would show you the max growth of new areas.
I am schedule to take my eighth session and laser does work. Except for a few stranglers, my upper lip is completely hairless, and my chin is following not too far behind.
Oh yes, the only day I would shave against the grain in on the laser day. I'm pretty gentle on my skin and have never had problems with cuts or scratches while shaving. And I like to use the Mach3.