It’s perfectly legal but personally, I would not find this really ethical: a lot of people don’t know F-Droid and if they find your application directly in the Play Store, they won’t know they can have it, the exact same application, for free but elsewhere.

I prefere one of those solutions:

• The ability to send a donation, it’s a very common thing.
• Having the same application twice on the Play Store, one for free and one with a fixed price (I don’t remember which app do this but I saw it once).

Of course this is my point of view, everyone has its own vision of what is ethical or not. Do not take my comment as the absolute truth!

Free software is a matter of liberty, not price. It is perfectly legal and ethical to sell free software. Keep in mind if you’re using third party code (whether it’s libraries or external contributions to your application) you must abide by the terms of whatever license it is under, this is whether it’s paid or gratis.

It’s even perfectly legal to fork an existing free software project and sell it on the play store, although whether that is ethical or not is up for debate - depending on what efforts you put into your fork before selling it, an orthodox Stallmanist might have no problem with it but the original developer(s) of that code may perceive this as “theft.” Keep in mind you must abide by the terms of whatever license the project is under, so if it is a copyleft license like the GNU GPL you must either provide corresponding source code or an offer for such.

Conversations, an XMPP chat app, does exactly this.

Sure , indeed there are some foss app that are the same as you described