Could you confirm me there is no specific exchange IDs for EEX and that it is necessary to use the Eurex ID (EUREX_XID and EUREX_RETRANSMISSION_XID)?

EEX is only another control segment on the Eurex-backend. The same IDs will be used in Eurex. Make sure you have a member-ID for EEX (which is not the same than in Eurex) and a special traderID.

Is there only one ( not two ) gateway to send all instruments for EUREX and EEX place? If yes I would like to know how can I find out if an instrument is in the EUREX or EEX place.

EEX-members have a separate memberId and traderId.

Will the newly cascaded trades information in the 'inquire position detail request' be available on the same day as the expiry date or will it be the next business day? What time e.g. 11pm are the cascaded trades produced? Are they produced in the Eurex overnight batch run?

The cascaded product expires in the Eurex Batch and Eurex sends out a Back Office Information, a contract change message. Also you can receive a Trade Confirmation with the posTrnTyp 126. In the next business day you can read the new position via Inquire Position Detail and in see the details in the CB010 and CB105 report.

Are there specific EEX Requests in the Values API document?

The EEX requests are included in the Eurex Values API, named as EFP trades The Values API Documentation can be downloaded from the WebPages http://www.eurexchange.com/technology/api_de.html