
I always count from the first mating, although of course, conception may not take place then. I don't scan and I'm really not going to get into all that again other than to say if both are healthy, the male is a proven dog, I assume there's a pregnancy and plan for it. You'll see puppies moving around by week 7. A scan only confirms, or not, a pregnancy at the time of the scan. And it's not accurate. If her due date comes and goes, then you see your vet for him to examine her and maybe x-ray to see if she is empty or not. And if you take her in for a shot to clear out any retained birthing material immdiately after you feel she's finished whelping, that takes care of that (need to know how many).
Vets (or another person) are happy to scan because it means income. As I've said before I don't want to risk stressing my pregnant bitches (and whatever anybody says, it is stressful for a bitch to need a car trip /vet visit) or risk her picking up infection. Sick dogs visit vets.
ps Don't worry about 'only' getting slip matings. Of course we like to see a tie, but it's not necessary provided there was penetration - one of mine only ever achieved a slip mating and his strike rate was 99.9% - he only missed to one bitch and she missed to another of my males the next season, and another male when they tried again at the next season. Clearly this wasn't meant to be (her!).