Here's one quick link on how they cut granite:
https://sciencing.com/granite-quarried-ancient-egypt-6032.html
Perhaps they used diamonds, which are harder than granite:
http://www.theglobaleducationproject.org/egypt/articles/petrie.php
Or maybe they used sand:
https://www.pbs.org/wgbh/nova/lostempires/obelisk/cutting.html
The exact technique may remain undetermined for now, but hardly mysterious.
As for gold on the statues, they weren't plated, they were gilded. Much like gold leaf, or the gold inlay on fancy medieval suits of armor. No electric current needed.
Here's a detailed piece on ancient Egyptian goldsmithing:
I think the most probable method that has made the most sense yet that would fit into their capabilities would be the bronze edged swinging pendulum. While this points to the Mycenaeans, I think it is very possible the Egyptians may have used the same method. It would definitely be within their limited technology level yet work well.
But there are indeed some anomalies in cutting work that truly cannot be explained such as core drilling and cores uncovered that were truly part of the ancient construction at the time, same in South America.
https://www.sciencenews.org/article/how-backyard-pendulum-saw-sliced-bronze-age-mystery