They can still have their umbilical cord up to 3 weeks from what I've read. Mine usually lose it around 1-2 weeks.
I've had to clean pasty butt at a couple days... I just made sure their bums were nice and wet with warm water and just used my nails to pinch itty bitty pieces of poop (meticulously - little by little) until I could see their vent. I had to use Q-tip at one point just to ensure I could see what was attached to what. The poop will dissolve fairly quick if you stay on top of it. The cords could be stuck on with the poop.
Oh and from my beginning experience... too much heat can be culprit if you are using a lamp vs a chic brooder plate. I damn near killed my 1st chicks, being so worried about heat. Since, I've only used a panel and haven't ever had them in house. If I don't breed my own, they start in the garage and go into the coop at 3-4 weeks (if not integrating into an existing flock, as long as it's 50 degrees or so.
I've watched mama hens take them outside on day 5 into 30 degree weather for hour long field trips with the occasional warm up.