When I click on single step, does single step interrupt generate? May be. In general there are 2 strategies. One uses single step interrupt. The other inserts a software interrupt at the next instruction of the source code and then executes a "run to break point without interrupts enabled".
Is the single step interrupt service routine in monitor code that lives in internal ROM of the microcontroller ? Yes.
Is the address of single step interrupt service routine in interrupt vector table? Yes.
How does this address get in the table ? When you start a debug session, downloading of the monitor firmware always programs the fixed vector table. The user fixed vector table is moved to a different address.
Please explain the single step activity behind the scenes ? That's not easy to explain and not really usefull.