APK files are described as similar to EXE files on windows. then you just need to download the app’s APK file and try installing again. In some cases you cannot download due to errors like insufficient storage etc.
You can download any kind of unsupported or non-downloadable apps (conditions apply). But the truth is, you can easily install any application on your device using google chrome.
Yes, Google always says to use their app store for installing apps for security reasons.