"facebook is a private company that can do whatever they want" – as much as i like the argument, i don't think it applies here. In the US being banned by one or few bug tech companies is almost similar to being banned by USPS, or by a store chains like safeway, walgreens or cvs. This should not be taken lightly and there should be legal protection against bans like this.

His activity of developing the tool was outside of facebook use as a user. Its ok if they ban his dev account, or the app(if it was a fb app) or try to block it.

Ideally, such cases should be tested in court, but there is such a huge imbalance between opponents, that it seems UK system is inadequate in equalizing it.