I was wondering whether I could install an app I create to cater to my personal needs solely for myself? Like a private app! (I know there are other applications to do this, but I want to learn something in the process)
So the question can be boiled down to
Can I install an app I created only on my own device?
Yes you can! If you create the app yourself you are not forced to share it on the Play Store. To actually install the app you will first have to accept apps from unknown sources in your settings. This can generally be found in the security section of the settings. While the Play Store is the most popular app store on Android (I assume), it has nothing to do with android itself. You can find apps on alternative app stores or even on forum boards or in email attachments.
If you don't share your app in any way, you will be the only person with that app.
Of course, once someone gets access to the apk file it becomes trivial to install it on another device.