1. MMS is not an SMS message but a GPRS message. correct ?
It uses a packet data transfer mode.. GPRS, UMTS or ANSI (CDMA/TDMA) equivalents.
2. MMS notification is an SMS message.
Yes.. a WAP push sent over SMS (a glorified URL).. the phone then pulls the data from the specified URL.
3. WAP over SMS. What does that mean?. Aside of the MMS notification issue, are there any other WAP over SMS issues ?
WAP is essentially a concept of HTTP post and get in a mobile data model.. WAP over SMS is a use of that push and pull model using SMS messages. But most WAP browsing operates on data sessions incl GPRS and faster. I'm not aware of there being much use of WAP over SMS.
4. SMS according to GSM 03.40. If an MMS notification is an SMS message. What is its IEI ? It has no specified value in GSM 03.40.
Not sure what you mean by IEI.. a WAP SMS message is encoded in GSM MAP like any other but contains special formatting (UDH information elements (IEs)) that pass specific src and dst port information so that the phone knows its a push message.