I would encourage them to go with a traditional battery operated opener in case of a power outage. My system runs on a 12V lawn tractor battery that is kept charged with a 30watt solar panel. These components are so inexpensive I can't imagine burying wire to charge it. Using the charge controller that is built into the Mighty Mule panel the battery lasts 5 years. You can almost set your watch by it. The opener panel has an alarm to let you know when the battery is getting weak long before it is too weak to open the gates.
If you decide to go the wire method you will also want to consider the depth to bury the wire. You don't want 120V on any gauge so shallow that it might accidentally get dug into. IMO not only is the wire method not cost effective, it creates a tremendous risk.
For lights you might consider some regular stand alone solar charged units.
I just bought a pair that have great reviews from Amazon for less than $30.
Aootek 182 Led Solar outdoor motion sensor lights upgraded Solar Panel to 15.3 in2 and 3 modes(Security/ Permanent On all night/ Smart brightness control )with IP65 Waterproof with Wide Angle(2pack) - - Amazon.com