Those chicks will need supplemental heat for a while (at least a few weeks.)
You could brood them in the house, or divide the existing coop and brood them there.
Chicks need warm enough temperature, and protection from heat/cold, wind/rain/snow, predators, older chickens. If you can provide that in the coop, they do not need to be inside your house.
For warmth: one area about 85 degrees Fahreneheit, the rest of their space at whatever temperature it naturally is. The warm area can be provided by a heat lamp or brooder plate or any other safe source of heat. The warm area needs to be big enough for all chicks to warm up or sleep at the same time. The unheated area can be as large as you like, with bigger generally being better. It is very important for chicks to be able to get away from the heat: that keeps them from overheating, and lets them adjust themselves to cooler temperatures by spending time in them. Chicks will naturally go to the warm place when they are cold, and cooler places when they are too hot.
For food, the "flock" food you use for your Silkies will probably be fine. Small chicks cannot eat big pellets of food, but if the food is small enough for Silkies it is probably small enough for those chicks as well. Check the label: the chicks should get at least 18% protein, with higher being fine. The calcium should be around 1% (layer feed is around 4% and is way too high for chicks.) If the protein and calcium are right, and the food is labeled as being for chickens, the other details are probably fine too.
