If there are millions of questions, will there be performance issues?

Performance of any service like this depends on the database in use, the underlying hardware specs, server connection speed and how well the database is optimized for this.

If you put this forum on a raspberry pi and have a database that is several GB, it wont be a great experience. However With decent hardware, huge amounts of sql entries (talking gigabytes of data) shouldnt be a problem for mysql or postgres if the underlying structure is decent.

Realisticly though, you will never reach a point of choking because of the amount of data you would need for that to happen.