There's the Profile Manager plugin (https://elgg.org/plugins/385114) which could be used to add new profile fields (can be made mandatory at account registration). But I don't think you can make conditional profile fields (i.e. depending on the selection of one field there a different additional options displayed).

The "Full age restriction checkbox" plugin (https://elgg.org/plugins/791444) is a simple plugin adding just a checkbox to the registration page. There's also no data saved (user input - or non-input - is just evaluated and either the registration proceeds or gets blocked). But maybe you could use this plugin as a starting point and just add the conditional input fields code and the data saving. Maybe the additonal profile fields could still be managed by the Profile Manager plugin (now without setting them to show on registration) as then it would automatically get them displayed on profile pages and they would be searchable.