Mennonites can. There is a spectrum of allowable technology usage and many crews are made up of different variants of faith so that they can be more efficient.

Yes. They use battery powered tools. They also ride to job sites in work vans. I’m not sure who plugs in the batteries though - maybe a designated heathen? Another fun fact - many use cell phones. One of the oddest things I’ve ever seen is a horse and buggy rolling down the road with a guy inside talking on a cell phone

What technology is allowed is decided on an order by order basis. Around here electric in the house is always forbidden for Amish as far as I know. For battery tools and other electronics there is usually a designated shed or barn that has electric, possibly shared by multiple homes. Any devices live in that building when not in use. There is a set time window during the day that they are allowed to be used and they must be back there by the devices curfew. Orders might limit the hours power is on in that building also. There will also be rules for how they can be used when they are in use as well.