First, you should use a newer openLCA version, especially since openLCA 2.2 has a way to directly connect and download to any soda4LCA source that is accessible on the web.
To your questions:
Does the OpenLCA elementary flow reference list have a document with all their available ids?
-> no but if you create a database with reference data, you have all the referfence data (and can check the flows e.g. by select * from tbl_flows in the sql window)
Does the ecoinvent 3.9.1 adapted to OpenLCA have a document with all the available elementary flow ids?
-> Same as above but check this with a database in openLCA that contains ei3.9.1
Does the elementary flows inside ecoinvent 3.9.1 in OpenLCA have a proper mapping to ILCD EF 3.0 and could be exported that way
-> openLCA lets you apply mappings, also in export, a database created in openLCA with reference data contains default mappings to several other systems, if these are "proper" is a bit a matter of definition.
edit: Thank you for your comment, the default mappings are here (for a database with reference data):
You can also copy and edit them.