I think that what you call multiple primary keys is a composite key. Right?
You have some options.
Use api/questions/dates/:date/types/:type
Maybe, the best alternative for you is:
api/questions/dates/{:date}/types/{:type}
This is more natural to read as a http resource for your case, even if don't make sense have a api/question/dates/{:date}
in your application.
Use api/questions/:date/:type/
Another alternative is:
api/questions/:date/:type/
Use query parameter
If it's no a problem for you, instead of return a single object question you can return an array of questions as response using a filter query, like:
api/questions?date=2022-10-27&type=XYZ
Both are not mandatory, but if the user send both, the return will be always an array with a single element. Also this bring some flexibility to your API, because the user can inform just one of them and have some results. You need to check if this behavior it's valid for your case.