IMEI is provided by equipment manufacturer for the mobile. It is stored in EIR via the network operator while registration. IMSI is a combination of MCC(Mobile country code), MNC(Mobile Network code) , MSIN(Mobile subscriber Identification number) and is stored in SIM. There are several such identifiers based on the mode of operation to uniquely identify a user.
GSM is a combination of TDMA/FDMA. Each BS is assigned one or more carrier frequencies which is then divided in time, using a TDMA scheme, into 8 time slots. The time slot usage is such that the mobile does not recieve and send it the same time. That is, the MS uses one time slot for transmission and one for reception.
The BSS acts as a radio resource manager and allocates a traffic channel (a radio channel and a time slot) for every MS once authenticated and informed by MSC. Each MS operates only over the provided radio channel in the given time slot.
In GSM, the RR protocol between the MS, BTS and BSC(BSS) does the routing of the data to the recipient and you can consider it to be similar to that of network layer(layer 3 of OSI). The routing of data is further coupled with SCCP for end to end addressing/routing in SS7.