I've only heard of a limited registration, and I think it's a registration that comes with a spay/neuter contract.
The 12 week rule is that the pup is better off to stay with the mom until 12 weeks of age. This way the pup learns from the littermates and mom and becomes more socialized. An example is the mom doggie helps teach that nipping hard is unacceptable. There are more specific posts here about the rule.
"Limited Pedigree" just means that if you were to breed the dog you would not be able to register the pups with the AKC. It's usually combined with a spay/neuter contract. Almost all reputable breeders sell with this kind of contract. The twelve week rule means that your pup shouldn't come home until twelve weeks of age. Depending on the pup some will let them go at ten to twelve weeks but it's a personal choice.