it looks like Airtable doesn't support combining formulas with lookups
Airtable does support using lookups in Formulas, however in your case, your lookup won't be a single value, but multiple. Airtable Formulas currently work best when they act upon individual values, rather than a combination of them. So yes one of the solution avenues is to split question and answers out into individual field values so that you can calculate them cleanly with formulas.
But given your current schema, scripting is another path forward. Scripting tools make use of JavaScript, which has plenty of tools available to convert between data types (such as making a comma separated string into an array), retrieve values in multiple tables, and/or run the necessary calculations. Learning JavaScript is worthwhile and multi-purpose, but if your time is limited, you might considering hiring a developer to help.