Android is an operating system, currently developed by Google, which is installed on millions of devices such as smartphones, tablets, smartwatches, televisions, etc. Although it is based on the Linux Kernel, Android has proprietary components so it is not free software (or at least not in its entirety).
To define the scenario we are in and about, let's say we have a device with a working version of Android installed (this is the typical case when we buy an Android device). That device is ready to work but may not have all the software we need and we will have to resort to installing it later. The applications that can be used in Android are based on a package management system that allows us to automate the process of installation, configuration and updating. The name (package management system) is due to the fact that the programs are distributed in the form of "packages" (with APK format in the case of Android), encapsulated in a single file that contains the files necessary for the correct functioning of the program in question and, in addition, includes additional information such as version, description, dependencies,...
To install software on Android, simply download the APK file, run it and follow the instructions in the installation process. As this practice seems risky (anyone can send us an untested APK that can produce undesirable effects in our system) Google has implemented a software "shop" from which we can download the programs we need (some free and others paid) in a simple way and from a controlled and secure environment (presumably). This "shop" is called the Google Play Store (https://play.google.com/store). The Google Play Store is more than just a software repository. It is a digital software distribution platform (for Android devices) and an online store that offers us other types of "products" such as films, music, books,...
Google Play Store is indeed a repository of software (among other things, as we have mentioned) but, for the most part, the software it contains is proprietary, even the free software it offers does not allow you to download the fonts. So the answer is NO; Google Play is NOT a free software repository. In addition, there are other limitations imposed by Google that we may not like (such as requiring a gmail account in order to access the Play Store).
If our intention is to have a repository of programs for Android, which are free software or open source and do not require us to "sign up" or have an associated email account, our choice should be F-DROID (https://f-droid.org/es/)
F-Droid cannot be downloaded from Google's Play Store, so we will need to go to their website, download the APK and install it manually on our system. The download path for the latest version is https://f-droid.org/FDroid.apk
If we prefer, we can use a QR code to proceed with the download:
Once the APK file has been downloaded, we will proceed to its installation, locating it in the corresponding "Downloads" folder and executing it (by clicking on it). For this procedure to work, we must first tell our device that we allow it to install programs "external" to Google's Play Store since, as we have already mentioned, Android by default only lets you install software from its own "store". To do this, go to SETTINGS, generally in the "Security" section, look for the "Unknown Sources" option (allow the installation of applications from other sources than the Play Store) and enable it.
Once installed F-Droid will have access to a complete FOSS (Free and Open Source Software) repository containing all types of applications and games. We will also have access to a help forum, project documentation, tutorials, etc. They will even explain how to set up our own software repository (with repomaker).
But that's another story....