POV using ATmega328 powered with cr2032 cell I am planning to make a POV (persistence of vision) display using ATmega328 with 5 red LEDs for display.
Below are my aims:


I want to power it with cr2032 coin cell, so power consumption has to be taken care, I am ready to keep single or 2 coin cell in parallel to meet current requirement.


Using 8MHz clock instead of 16MHz can help


Does it require separate boot-loader to be installed?
During boot-loading do I require to put external 16MHz clock?
How to ask controller to use the internal 8MHz clock?

Supply voltage of 3V instead of 5V can also help, and cr2032 gives out 3V 


What care should I take while using it at 3V?
Any mechanism to set the threshold for controller to stop working?


To reduce the weight of whole circuit so I can rotate the board using small toy motor (I don't have a gear box).
I am planning to control the speed of motor using LM317 voltage regulator as a constant current source.
I will mount the LEDs on straw, keep the controller and the coin cells at the center. (Guessing that will reduce the torque required by the motor as torque=Force*radius and weight being at center reduced the radius)
I am okay, if this circuit works for just few hours OR days.
Not exactly an answer, but too big to place into the "comments" area.

Clock
For the 8MHz vs 16MHz, you should be able to run your project at 1MHz. Just use a bare AVR MCU with the Internal 8MHz oscillator divided by 8 - search for AVR Fuses. You can program it using an ISP (or and Arduino as ISP)

Battery
About the CR2032 or coin-cells in general are not designed to constantly supply current. You can use it for very low currents, up to 2-4mA or in pulses. Otherwise you damage the cell, reducing it's total usable capacity. Maybe have a look on sub AAA batteries instead of coin-cells.

Motor
For the motor, have a look on the micro coreless dc motors. They are really tiny and should offer an excellent efficiency. Motor example

Motor Driver
Not sure about the LM317. You don't want any kind of regulation as it would waste energy. To drive the motor a small Mosfet should do the trick. You can control the Mosfet using PWM, which will define the motor speed. Don't forget to implement some kind of rotary encoder to count the motor RPM so you can precise speed control - a tiny magnet and a hall-sensor should be enough.