Do you run any statistics on what operations are triggered how often via you app?

No, I don't run any statistics.

I also think you should start demanding small, rather cosmetic, fees for certain services of your app, like conversions, steem engine toke claiming/staking etc.

Thanks, I like the idea, but it would only be possible for operations that require an active key. The question is, if people would than still use SteemWorld for those features. I will keep your idea in mind.