I've read mention of hens moving and or stealing eggs from other hens by scooping them up and holding them between their body and wing to move them and I've heard of them also rolling them between nests if the nesting boxes are 'open'.
As for introducing a clutch of new chicks to a flock is always risky. I've done it before with no problem. Mom made the decision to break through the temporary fencing and escape to free range with the flock. But every flock is different. The question I ask myself is 'is this chick old enough to survive a peck from a hen or rooster? Or big enough that it can get out of the way?' My chicks are almost 4 weeks old now and momma is paying less attention to them every day. She will probably rejoin the flock soon but the chicks are going to stay in the 'nursery' coop for at least 2 more weeks before I let them out under supervision. Yep, it's extra work, granted, but there are posts here on this thread from folks that have lost chicks to aggressive behavior. Some chickens do not recognize chicks as being one of their own kind.