Partitioned tables and triggers

Hello to everyone, yesterday I created my first montly partitioned table with
its insert trigger following the specific manual page.

At the moment table seems to work correctly, but I have some doubts:

1 - After an insert operation, I can see data either in master and in child
table. Is this a normal behavior?
2 - I created only insert trigger, but not update and delete. Do I need also
these triggers to managing data correctly?
3 - When a BEFORE INSERT trigger function execute in its turn an INSERT
operation, are the origina INSERT executed or not? Are the data inserted in
master table also, and not only in child table?

Thanks in advance.

Mephysto

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