1) Vector address provides either the ISR or ISR address to the processor. You have look to through how an ISR routinue is called up on based on vector table.
2) All of these are quiet bit different.
Reset vector is just a pointer, on press of reset it points to the start of the program.
Interrupt vector is memory address of an interrupt handler in vector table as said, you have a lot many kinds of interrupts based on the processor and its handling ways , and wouldn't be enough to produce it here. You have to get through some books for its detailed descriptions.
Simply, when an interrupt is generated, OS saves its execution state in Link Register, and begins execution of the interrupt handler at the interrupt vector.Program counter sets to vector address. A link register helps to returning from completion of interrupt execution.
stack and paging - refer to wiki it a lot more info.
3) Which processor are you referring to ? Each processor has seprate method to execute.