Questions about indexes

Hi everyone !

I have some little questions about indexes :

Does PostgreSQL create an index when a table is created?
Does it create index even if there is no PK for this table?
If yes, why?
I know that indexes increase performance for SELECT but it is the
contrary when INSERT because the index must be actualised every time,
isn't it?
How can I see all the index that PostgreSQL have implicitly create?
How can I delete them in keeping integrity in the database?

If someone could answer these questions, I thank him in advance.

Sincerly, Renaud THONNART