I think it’s a good analogy to say that Android has become the new Windows; the most widely used platform. And what’s PortableApps.com for Windows, an independent platform that provides a great selection of free apps through a handy interface, in the Android world, F-Droid seems to have emerged to fill this role. As Android is not equal to Windows, F-Droid is not equal to PortableApps.com. Let’s get into it!
Oh, and please don’t come with how everyone is running a Linux desktop! Maybe your team does, all your team, but if with F-Droid you only aim at people running a Linux desktop, and your target market doesn’t include folks who just prefer free (or portable) software on Windows, you aim too small with the project.
App selection and discovery
Windows has been around for 20 or so years, and you can find most of the great, free apps you’ll ever need on the platform on a single page, divided into categories on Portable App Directory (over 400 free) - PortableApps.com.
Android has become mainstream in, maybe the last 5 years, and if you ask me, for the direct, tried and true Android equivalents of the great, free Windows apps collected on Portable App Directory (over 400 free) - PortableApps.com, I’d be in trouble. In Android land there seems to be much more apps, apps developed by smaller teams, or even just one person, the average app you use might be at a much less sophisticated stage than its Windows counterpart (don’t forget: the Windows platform had 20 years, mainstream Android is around for 5 years or so), many Android app projects are abandoned by their developers (I just read about the great purge here). All in all, and unlike for Windows, for the Android platform, some kind of app discovery aid and rating system seem to be necessary.
The large amount of available Android apps (or smartphone apps in general) compared to the average number of apps installed on the average smartphone user’s phone, especially the ones which are of actual use or value to her, compared to how these numbers work out in the desktop world is also worth noting.
The obvious rating system for Android apps is the Google Play Store ratings. For a starter, can we just get the Google Play Store ratings embedded onto this site in a neat form? Because what do we find on F-Droid? A huge list of (mostly unknown) apps loosely organized into vague categories (think of all the PortableApps.com apps fit on a single page) in alphabetical order, quite a few of them are abandoned, or haven’t been updated for long years (I know; the great purge just supposedly happened).
The people who visit and the Google Play Store and rate apps there are a different group of people from who visit F-Droid and would rate apps over here. So F-Droid could have its own rating system; why not? Also app discovery could be more nuanced than the top apps being the ones coming first in the alphabet. Some kind of online shopping algorithm could be utilized, similar to Amazon’s search (there are open source alternatives), what’s hot, what’s searched for by more people is on top, what’s rated higher ranks higher. Of course, everything in the F-Droid store is free (I’ve see some paid for upgrades for wallpapers here).
The rating system I suggest is a simpler one that the old 5-star ratings: thumbs-up, thumbs-down, and meh: Netflix Is Ditching Five-Star Ratings in Favor of a Thumbs-Up
It would be also neat to find more apps by the same developer; similar to how you can do the same on Google Play and iTunes.
Who is/are F-Droid? There are a bunch of names on your site, but no one seems to be highlighted as team leader. F-Droid is a nonprofit. I see absolutely no reason for you guys to be a nonprofit. OK, you are these nonprofit folks at heart; I get it. Then by all means, why don’t you incorporate as a social enterprise, B Corporation, or something like that? PorableApps.com is founded by John T. Haller (the name and the face you can associate with the idea), and he set up a for profit company for his venture, Rare Ideas, LLC. Do you have Twitter, by the way? On your home page I’ve only found some Twitter clone no one really use.
How does a project gets added to F-Droid? For example I happen to know the fine people of the popular, open source media player Kodi, would totally love their app to be on F-Droid. Does it more depend on you or them, who has more work to do to be included?
This other, neat project wants to be in, too: Add to f-droid · Issue #37 · mpv-android/mpv-android · GitHub
Is it more up to you, or more up to them?
Would it be a totally against everything you stand for to possibly later on include 100% legal, supplied-by-the-developer freeware APKs, just like PortableApps.com do? They also started from open source only, then embraced legal freeware as well. For a notable example, take Foxit Reader. I think it would be a neat addition; everyone would gain from it; developers, users, and the platform as well (depending on your core values). I’m not talking about gray APKs, such as the ones on Aptoide, but the 100% legal ones. Just like how PortableApps.com rolls.
By the way, Aptoide has no real community. Both you and PortableApps.com have.
The bottom line? This is a little philosophical question: Do you want to be right or popular?/Do you want to be more uncompromising or a little more widely distributed? And how does your choice compares to the route John T. Haller of PortableApps.com has taken?
One related issue. For all APKs the home page offers a PGP signature. Except for the most important one; for the F-Droid app store APK. I understand various open source projects keep different emphasis on proper documentation (some care more, some care less), but in your opinion, what % of your users can do the verification on their own (especially by heart, without consulting 3rd party documentation)? On the other hand, if you added a simple SHA checksum, to what other percentage of your users that would be useful, and good enough; what percentage of them knows what the heck to do with it (without consulting 3rd party documentation?). Again, do you want to be more right, or a little more popular and useful for the masses?
So called repositories. Should a simple user know, care, and distinguish between the F-Droid Repository, the Old F-Droid Repository, the Guardian Project Repository, and the Old Guardian Project Repository? Maybe yes, maybe no, maybe something in between, such as this could be simplified for the end user on the outside and can be only seen from the back end. Good documentation could also help explaining the user why you just can’t put every app on a single page, just like PortableApps.com can on Windows, how Android (and F-Droid) is different, has to be different? Do you want to be more right, or a little more popular and useful for the masses?
Some related food for thought: Madhurjya Roy’s answer to Which version of Linux does Linus Torvalds use and why?
If you ever expect some funds to arrive onto your back account, you should display the name of your bank, and perhaps your account’s currency, for proper bank transactions. If I understand, quite a few of your team members are of Spanish origin; so why don’t you set up a euro bank account? That applies to a much bigger audience than an account and the currency they use on that funny island where they also happen to drive on the wrong side of the road. 
Oh, and and also don’t forget to keep up the good work! 