F-droid is an alternative app store, that only features FOSS(free and open source software). It respects your privacy and anonymity. It doesn't send data anywhere and no login or registration is required.
For an application to be approved by fdroid, the source code is examined so as to be fully free and open source. Also fdroid lists any kind of "anti-features" that an app might have. Like if it contains trackers, ads, known vulnerabilities, non free parts etc.
Can you survive only on fdroid? Yes you can, in fact since I last performed a factory reset on my phone I haven't used the play store once. All the apps I have installed came from fdroid and I'm doing fine. That being said not all apps you find on the play store will be available on fdroid. An example is signal.
To download fdroid go to f-droid.org, download the apk, enable download from untrusted sources. Don't be worried, I would say that Fdroid is much more trustworthy than the Play Store or the Apple Store. You'll need to allow fdroid to install apps as well. Enjoy