DMS transaction

You should be able to insert data to target database as long as you are not breaking any referential integrity with other tables. Other things to look is if your table has auto fields like identity or sequence it might clash with the inserts coming from dms and thereby generate duplicate ids. and if it is primary key it would fail this inserts.

This would be achieved by using ongoing replication. If you are already choosing the DMS migration type as "migrate existing data and replicate ongoing changes", the data would get migrated as of start time and any changes that are in the source database CDC log would get replicated into the target database.

If you are just choosing DMS migration type as "migrate existing data", you would need another replication task using DMS.

Please check this link for more information: https://docs.aws.amazon.com/dms/latest/userguide/CHAP_Tasks.Creating.html