questions to power consumption

• Is my take on the power consumption correct?
  
  

I didn't rework the maths, but it sounds about right. In reality you'd hope the display update would take less than 2 seconds as well.

• Are 2.4v enough to drive the pico?
  
  

Just :) It'll run down to 2v, but the voltage regulator will drop maybe 300mV. You could connect the batteries straight to the 3.3v line though.

• Is it possible to control the VBAT Pin to only activate at designated timer?
  
  

No, but the IO pins will supply 20mA, so as long as the display didn't peak above 8mA then they should be good enough.

Also, the display itself may only draw 8mA when writing - it may be much less when idle.

Hope that helps!