What is the rate at which a mobile/cell phone listens for an incoming call or a text in standby mode?
In most cellular systems the receiver in the handset (mobile, phone, etc.) goes into a low power "discontinuous receive" mode when not actively in a call.  It wakes up about once per second and listens to a control channel from the base station it's currently associated with.  The operations inside the handset occur at whatever the CPU clock rate is, on the order 26MHz, 38.4MHz,... or higher.  The timing at the radio side of the system is fixed to certain symbol rates, but once messages are received the internal processor can operate as quickly as it is capable of (and designed to operate). 

If there is an SMS (text) message or a call for the handset then it can be delivered in one of the base station control channel time slots.  Since it's a synchronous system, the timing is really governed by the design of the cellular system rather than the handset.

What level of detail are you interested in?  Once the message is received, it's up to the phone software to alert you that a message has been received, and that's dependent on what else the phone is doing (schedule priorities, interrupt rate, etdc.).