Hello,
Thank you for your request.
Regarding attribute search, there is no more functionality than described in the corresponding help section: Use CityEngine Web Viewer—ArcGIS Online Help | ArcGIS
So please make sure, that all the classification the user might need (like "FLOORCOUNT < 2") is added as an attribute, before exporting the web scene.
Since there is no official support for a "proper DB query", the only way is hosting the Web Viewer yourself and modify the search code. But this needs extensive programming knowledge.
42471 - Host 3D Web Scenes