Hi,
You can monitor the below
1.replicaton monitor (in sql server management studio) available to see if the replication is going on successfully or not
2.check the replication jobs and history of the jobs (in sql server agent tree)
3.check snapshot agent status, log reader agent status and synchronization status
4.you can check the latecny by inserting a tracer token to calculate how much time is taken
to transfer data from publisher db to distribution db and from distribution db to subscriber db