Hi, border collie owner here. Pup should have had first set of vaccinations but definitely not the second yet. Your pup is very small, as in half the weight ours was at 8 weeks, so I definately think it's worth getting a vet check over.
Wet cat food will run right through my collie too, always has done, so from that side of things the loose stools is to be expected.
I would expect more energy than simply walking or getting over a step, we were having to get ours down from the back of the sofa and to stop trying to bounce onto the coffee table when he first came home. They are a breed with a LOT of energy, I've only seen ours lethargic when he was teething.
What did the breeder feed her? The upset tummy and unwillingness to eat could be a change of diet. Ours wasn't onto wet food when he came home, still on porridge, wheatabix or rice and little bits of chicken, so it's possible that the food is just not what she's used to.
Pm me if I can be of more help, my collie is still a pup, only 16 weeks, so I do know how nervous you are when they first come home, but your experience with the lack of energy sounds worlds away from what we've seen and for that alone I'd get her seen, collies love affection but at this age they're not really cuddlers, they're explorers, bouncers, want to see everything and be into everything.