How to determine if AD replication occurs:

cd "c:\Program Files\Support Tools"
repadmin /replsum /bysrc /bydest /sort:delta

How to see which domain controller is AD schema master operations role:

cd "c:\Program Files\Support Tools"
netdom query FSMO

How to verify if the schema operations master has done inbound replication of the schema since the last time the machine restarted:

repadmin /showrepl

The command to update 2003 schema to 2003 R2 is:

Note: this executable should be in the CD or folder where the update packages is. This command will update and propagate the schema. If you have less than SP1, you need to run the same command with /domainprep)
adprep /forestprep