While embedding Gecko in desktop applications is not as straightforward as embedding Chromium, Mozilla's GeckoView project makes it easier to do this on Android:
GeckoView is the foundation of Firefox for Android and Firefox Focus. The SmartCookieWeb-Preview browser, which supports sideloading Firefox extensions on Android, is also based on GeckoView:
But then again on Android the OS already provides a Webview implementation for usage by apps, so while on Android Gecko might be more easily emebeddable than on Desktop, it's then hobbled by the fact that on Android the choice for app developers is either using the default Chrome/Blink-based Webview provided by the OS at absolutely no size-penalty, or else thinking about shipping a full browser engine with your app at a size penalty of dozens of MB, at which point you might then consider possibly using GeckoView instead of shipping your own specific version of Blink.
No idea. With flash this certainly used to work (i.e. Adobe distributed an APK with the Flash plugin, and other browsers including Firefox were able to use the library contained therein), but of course Flash has been discontinued for quite a while now and I don't know whether a similar approach might still work with the most recent versions of Android.
In any case though this would raise the backwards compatibility constraints on Mozilla quite a bit, and I'm not sure whether they'd be willing to take on that burden. Of course even now they can't go around breaking GeckoView-APIs all willy-nilly, but when it does happen, it "only" affects app developers the next time they want to recompile their app with a newer GeckoView version.
If GeckoView was being distributed as an independently, user-installable library instead, any breakage at all becomes a big no-go, because users naturally expect their existing GeckoView-using apps to keep working regardless of which updated version of GeckoView they might happen to install.
https://mozilla.github.io/geckoview/
GeckoView is the foundation of Firefox for Android and Firefox Focus. The SmartCookieWeb-Preview browser, which supports sideloading Firefox extensions on Android, is also based on GeckoView:
https://github.com/CookieJarApps/SmartCookieWeb-Preview