This must be an Exalytics system, right? I ask this because compressed tables are not licensed for use outside of an Exalytics system...
As you note, currently replication is not possible in an Exalytics environment, but that is likely to change in the future and then it will definitely be the preferred mechanism for this. There is not really any other viable way to do this other than through the application.
With regard to your specific questions:
1. A backup consists primarily of the most recent checkpoint file plus all log files/records that are newer than that file. So, to minimise the size of a full backup ensure
that a checkpoint occurs (for example 'call ttCkpt' from a ttIsql session) immediately prior to starting the backup.
2. No, only complete restore is possible from an incremental backup set. Also note that due to the large amount of rollforward needed, restoring a large incremental backup set may take quite a long time. Backup and restore are not really intended for this purpose.
3. If you cannot use replication then some kind of application level sync is your only option.
4. Datastore and database mean the same thing - a physical TimesTen database. We prefer the term database nowadays; datastore is a legacy term. A DSN is a different thing (Data Source Name) and should not be used interchangeably with datastore/database. A DSN is a logical entity that defines the attributes for a database and how to connect to it. It is not the same as a database.
Awesome, thanks Chris. Yes you're right, Exalytics.