questions to power consumption

i am an absolute beginner (and even worse with an enterprise programmer background) and thankful for every hint and critic :-)

for my version of a word clock i am trying to use an e-paper display with an espruino pico

the display is this one: http://smart-prototyping.com/NOA-Labs/E-­ink-E-paper-new-version-display-module-3­.3V-2.04-inch-177x72.html

so far i have the components and i am on my way to migrate (luckily provided from manufacturer, some quite complicated command sequences) the arduino code to espruino

the final goal is to run from battery, for this i would be thankful if someone can answer my questions

my take on power consumption

• assuming 2s operating time every 5 minutes (its a word clock, update every 5 minutes is enough for me), 24s per hour
  
• Pico deep sleep needs 0,02mA/h
  
• Pico operating needs 32mA/h
  
• Display operating needs 8mA/h (but it is an e-paper, power is only needed to update the display, content stays after that)
  
  

Pico current draw in mA/h = 0,23 mA/h = (0,02mA/h:3600s*(3600s-24s)) + (32mA/h:3600s*24s)
Display current draw in mA/h = 0,053 mA/h = 8mA/h:3600s*24s
final power consumption ~ 0,29 mA/h

• assuming 1900mA/h from 2x AA eneloops (2.4v)
  
  • according to the specification the display works from 1.9v - 3.3v
    
    

operating time ~ 0,76 years = (1900mA/H:0,286533333 mA/h:24h:365d)

i know that is just a theoretical value, voltage drop will probably happen earlier

Questions

• Is my take on the power consumption correct?
  
• Are 2.4v enough to drive the pico?
  
• Is it possible to control the VBAT Pin to only activate at designated timer?
  
  • So far i think i need a transistor, but maybe it is possible without an extra component.
    
  • Are there alternatives to my approach? (can a GPIO pin drive the display? i am not sure about the current draw)
    
    

updated

• was 2s operating time per hour, but should be (60min/5min)*2s=24s