Can I have Oracle primary 11.2.0.1 and standby 11.2.0.3?
The physical standby database must be physically the same as the primary database and this means the versions must be identical.

A logical standby database can be any version, depending on how it is implemented. With 3rd party tools you can go from v10 to v12 and back. The restrictions here are on the data types that are to be replicated.

If this is for an upgrade, you start with a physical standby database, convert that to a logical standby for the upgrade.