Can I make a paid app on playstore free on fdroid ?

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!