How frustrating! Two occasions I have bought birds from breeders they have brought illness (respiratory and scaly leg mite) and it boils my blood
I began treating my girls leg mite with vaseline but she is a huge Orpington and too heavy for me to lift with one arm so it's extremely difficult without help, and then I noticed it begin on my other girls. I bought some Nettex spray and used this weekly plus the vaseline when someone was home to help me and it did the job. Her feet might still look a bit scaly until they naturally molt - try and trust your gut when you think she's clear - and then treat for another week or two. Keep a close eye and if starts to get any worse at all treat again for another couple of weeks.
Personally I would take the Pekin to a vet - infected lumps may need antibiotics and rule out any contagious diseases.
For lice/fleas dusting with diatom and adding it to their dustbaths is a good place to start. Here in the UK many people use cat flea treatment (frontline), one small drop for bantams and 2 for regular chickens, on the back of the neck. I used 1 sachet to treat 10 ex-battery hens when they came with a huge lice infestation.
Good luck, I hope you get everything sorted and can really enjoy your new girls