1. A microprocessor supports a single hardware timer. Suppose instruction SET_TIMER permits one to set the timer value1. Does this need to be a privileged instruction?

No.

Explanation:

The Instructions that can run only in User Mode are called Non-Privileged Instructions .

Various examples of Non-Privileged Instructions include:  

Reading the status of Processor

Reading the System Time

Generate any Trap Instruction

Sending the final prinout of Printer

Also, it is important to note that in order to change the mode from Privileged to Non-Privileged, we require a Non-privileged Instruction that does not generate any interrupt.