Home automation is the residential extension of building automation.
It is automation of the home, housework or household activity.
Home automation may include centralized control of lighting, HVAC (heating, ventilation and air conditioning), appliances, security locks of gates and doors and other systems, to provide improved convenience, comfort, energy efficiency and security.
Warning: Working with electricity can result in injury, property damage, or even death if it is not done properly. Please keep this in mind while assisting others. If you are not sure about what you are doing, hire a licensed professional.
Do you mean regular ON/OFF? If so, I've already written about something similar... https://reddit.com/r/IOT/comments/17zaapw/easiest_way_to_control_batterypowered_christmas/ka16uej/
However, when it comes to controlling their functions... would need to know exactly what equipment it is and how it works in order to advise.
Depends if it has to stay battery powered.
If you're willing to hardwire it, get a battery eliminator kit like this (get the right one for your device, be careful!) and now instead of a bunch of AA/AAA powered devices you have a bunch of USB powered devices. Get a multi-port USB charger, plug it into a smart plug, and you're golden.
My wife has a bunch of these that all took 3 1.5v batteries, so I soldered wires into them to run back to a "hub" that plugs into a 5v microsd charger and they are switched with a simple outlet remote. It would be a good idea to make them not permanently attached to the hub for when it's time to put them away.
You could do it with a mix of 2 and 3 1.5v battery lights but you'll want to add an appropriate resistor. A 100Ohm resistor should drop it 2v at 20mA. It's kind of depends on how they're wired, mine aren't out yet. I don't recall if I added a ~25Ohm resistor to the 3 battery ones but I probably should have if there wasn't one already.
you could consider using smart plugs with built-in timers to automate the decorations. This way, you can schedule when the Christmas village lights up without modifying the items themselves. It's a non-invasive and convenient solution for battery-operated decorations.
I hope to power this sort of thing with a PoE network switch. I haven't tried it yet, but I think you should be able to force a certain voltage over Ethernet. If it works you could automate the interface to be enabled or disabled when you want