Hi invisible_zebra,
Welcome to the Apple Support Communities! Thanks for posting your issue here and we'd be glad to check this out further with you. We understand that you're experiencing issues when attempting to install third-party apps onto your Mac. We'd like to ask you a few questions to ensure we're on the same page with your issue. You mentioned that you're dragging these apps over to the "App Store icon," are you referring to Applications folder within the Finder app or somewhere else? You'll want to make sure they're being moved into your Applications folder.
You may also find the information in this article useful here: Install and uninstall apps from the internet or disc on Mac.
As for the apps you mentioned, these apps aren't available in the App Store. Not every developer offers their apps through the App Store, and they must be downloaded directly from their own websites. If you're still experiencing an issue installing these apps on your Mac, you may want to reach out to the app's developer for additional support. They'll be able to confirm if the app is available in your area or investigate on the issue further.
If you're able to download these apps, you may also need to install Rosetta in order to open the apps since you have a Mac with Apple silicon. To learn more about how to install Rosetta and how it works, check out the information in If you need to install Rosetta on your Mac.
We hope this helps! Take care.
