When I was there the power operated until 10pm at night. From that time homes would either run from personal generators, or batteries - to power refrigerators, lights, routers, etc. These days the homes have or are getting solar panels.

Internet was terrible at the time. I wrote about it here: https://bluishcoder.co.nz/2012/05/29/pitcairn-island-and-slo...

It has improved but is still relatively slow and expensive.