I think some people are confused/missing the point.
This isn't competing with F-Droid, it IS F-Droid. Everything from the statistics to the APK downloads (notice the redirect) are sourced from https://f-droid.org/.
It's a beautiful front end and necessary improvement over what exists, but it's complementary not competitive.
My $0.02:
1. Link to download button to the app entry in F-Droid so I can download it from the Android client. (Getting the user to trust random APKs is not a responsible behavior.)
2. Clarify that this site is a viewer for F-Droid and non-UI contributions should be sent there.
Other misc notes:
Install F-Droid as a system app (root) in order to install packages using the client without having unknown sources checked.
Your download links point to the most recent version of the app, which is not always the recommended version available from F-Droid. Recommended versions are marked with a star. For example, http://fossdroid.com/a/fdroid.html serves a download of 0.86 which is an unstable test version. All of this is handled better by the F-Droid client app. The way your site is set up now could lead to a poor user experience if they encounter problems with unstable versions of apps that shouldn't be downloaded by default.
Being open source, you're free to do whatever you like, but I suggest you talk with the F-Droid devs to make sure everything is mutually beneficial.
