I don’t know if I would cull and start over just yet, but the limping and the snotty nostril/sneezing is a little worrisome. Chickens can sneeze occasionally from environmental reasons, such as dust in feed or in the coop, and as long as it is not every few minutes, it may be normal. If the nostril has thick or colored secretions, that doesn’t sound good. If you lose or cull the sick one, getting a necropsy by the state poultry lab is a good way to find out if ahe had anything.
It is always a gamble to buy chickens from a breeder—you never know if they have had a case of this or that, and Mareks is pretty much everywhere. Wild birds can bring in respiratory diseases or you can have a chicken exposed at one point, then they might not have an outbreak until they are stressed.
I have bought a few from a breeder once, but in the future, I will only buy day old chicks from a hatchery. Even then, you still can end up with a disease.