Apparently, it is really risky to make your app an open-source as it can be used, duplicated, and even re-released by many anonymous users (but less likely due to the fact that you can easily report them). You can read more of pros and cons of making an open-source program here^[1]. Making it open-source would limit your capability of monetization, and would not let you have restrictions on to codes as well. But on the other side, if you would still do this as a start-up project, there's no lose with publishing it to be open-sourced.

Since this is just a mobile app, don't be bothered by the mistrust and doubts of people that doesn't want to risk downloading your app. I've already trusted this the time I saw you managed to upload this on Apple play store (which is a heck of security required for an app to be published). I won't insist for you to take the risk of making the back-end public. Either way, even anyone can still lookup on the codes of your app with Reverse Engineering. And yes, make your donation link/address prominent so that every visitor would know that no one is funding the development of your platform. Overall, Keep up the good work dude!

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[1] - https://www.reddit.com/r/androiddev/comments/1inegt/what_are_the_pros_and_cons_of_making_your_app/cb67era?utm_source=share&utm_medium=web2x&context=3