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.
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.