Does RAM support incremental replication? Is there a way for me to find out the set of changes(CRUD on assets, asset types, category schemas, etc) since I last synchronized?

RAM provides real-time access via Web or Eclipse clients. There is no concept of connecting 'off-line', which would require a replication scheme.

You can monitor Assets in RAM very easily for changes. Simply 'subscribe' to an asset and you'll be notified when the asset undergoes any CRUD type operation. You can also monitor assets via news-feeds, or you can use our friendly and fully documented reporting URL's to get access to complete audit history and details.

I hope this answers your question, talk to you soon.