MongoDB Balancer:move data inside replication set or across replication set?
1 - Yes, the balancing operation can affect the performance, that's why you can schedule the balancing window. By default, the balancer is enabled and may run at any time.

2 - The balancer moves data chunks between shards.

Just to clarify, each shard is a replica set. All members of the replica set (the primary and N secondaries) have the same data (replicated). Therefore, each shard has a different subset of the total data.