Filtering data in a publication
Assuming you are running transaction replication. This is how it works in your scenario


When initial records are inserted with replicated column value as 'N' on publisher no records will be replicated to subscriber.
Once you update the some of the records with replicated column value as 'Y' based on your logic on publisher only those 'Y' records will replicated to subscriber.
And for last question once you update any of the replicated column 'Y' value records on publisher back to 'N' in subsequent runs of your logic those records will be deleted from the subscriber.


All of these operations can be monitor by executing the EXEC sp_browsereplcmds on distribution database. In the execution results look for command column to see what exact is performed by replication process.