If you output both video and audio only on the external display you might save battery, but it will depend on your settings (resolution, refresh rate, audio quality, etc.)
When I have my MacBook connected to an external monitor through USB adapters, it does drain a little faster. I haven't tested if my HDMI monitor connected directly does as well, but I'm sure it would. Any external monitor should require some extra GPU resources which means more energy which means your battery should drain faster. How much faster depends on lots of things.
When you connect an external display to your laptop, the graphics processing unit (GPU) has to work harder to manage both the laptop’s built-in display and the external one. This increased workload requires more power.
The GPU must render the images, videos, and other visual elements on both screens, and in some cases, it might need to render different content on each. This extra processing effort consumes more energy.
Additionally, the external display might require the laptop to send power via the connection, depending on the type of connection used (such as HDMI or USB-C). This would also contribute to a faster battery drain.
Together, these factors lead to a higher energy consumption, which will cause the laptop’s battery to deplete more quickly than when using the laptop’s display alone.
They exist but they are rare. Most of them are USB powered small monitors.
If you're connecting your laptop to an external display it's usually via a hub/dock (powering your laptop too, making battery drain irrelevant) unless you're connecting it to a display in eg. a meeting room without connecting power separately and then GPU load matters
I'm having a 15" mobile external monitor for my business trips, which is powered through my laptop. At least for those mobile displays, this is quite typical. Often you just need one USB C convention for power and video
Yes, but just sitting there displaying a photo or something won't take significant battery. If you render 3D graphics or something, it'll crunch numbers like on your panel, of course.
Some will, the display backlight needs power after all and a fair amount. I believe most displays have either an internal battery, maybe some can draw power from the laptop. The former will have negligible impact on battery as the computer only needs to render the image for the second screen and send the video output the display, the latter will have a big impact on battery as on top of all that, had to power a big bright backlight.
I've connected Cintiqs, portable monitors and regular monitors to my laptop. I've never seen a DP or MDP or HDMI screen that didn't also have another power source, but maybe they exist. In any case those didn't seem to affect my battery much, because they were plugged.
I have a portable monitor that connects via usb-c, that one drains the battery but I usually use it with my laptop plugged so I can't really tell what kind of impact it has.
is it externally powered?
it has to get power from somewhere. If the only cable going to the monitor is the DP or HDMI cable, then yes. it's draining the laptop. VGA doesn't carry power- those would be universally externally powered. Though I'm not sure there's any laptops that have VGA outputs still.