Will the app still be on my old device? So recently a favorite app of mine has been taken down from Google Play Store. But even though the app is no longer available on Play Store, it is still on my phone and tablet (both from Samsung company) and works perfectly fine on both of my devices. Also, when I go to 'My Apps and Games', I still see the app on 'Library' and 'Installed' options.
I'm aware that in order for my favorite app to function properly, I must ignore software updates on my devices. Hence, I've been ignoring software update notifications ever since.
But what I really want to know is that, will I be able to install the app from 'Library' on a new device from Samsung or any other company even when it is no longer in Play Store? Or doing so will cause the app to malfunction across all my devices? Will the app still be safe on my old devices?
If an app developer removed the app from Google Play Store this does not change anything for device which have the app already installed. Google only discards apps from devices if the app is known to behaving malicious (and may be if the app is violating some Google [business] rules, but I am not sure about that). Therefore your favorite app will stay on your old device unless you device to delete it.
On a device you won't be able to install the app anymore. Therefore if you want to continue using the app on a new phone you have to extract it's APK(s) from the old device and install it/them on the new phone.
If you want to keep your favorite app I strongly recommend to you to backup the app now. However it may happen that the app is not compatible with the newer Android version of a new device or the CPU architectures supported by your new device (ABIs). In such a case you have to let the app go.
To backup an app I recommend to you not only backup the app but also the app data (if the app allows to do so). This can be done on a non-rooted device using Android Debug Bridge (ADB) using the command adb backup. See various posts here on Stackexchange on that topic.
The app APK itself can be retrieved by various file explorer tools. Extract the APK and save it to a secure location e.g. on your PC and/or an external flash drive.