What is RRCConnectionRequest in LTE?

It is the uplink LTE RRC message the UE sends to request establishment of an RRC connection.

What comes after RRCConnectionRequest?

The eNodeB responds with either RRCConnectionSetup if the request is accepted or RRCConnectionReject if the procedure cannot continue.

Does RRCConnectionRequest carry NAS?

No. The initial NAS message is carried later in RRCConnectionSetupComplete, not in RRCConnectionRequest.

What identity is used in RRCConnectionRequest?

The UE includes either s-TMSI when it has valid temporary identity context or a 40-bit randomValue when it does not.