Somehow the audio for this test is not playing making it impossible to answer correctly.
I agree. It is commonly used in American English, usually in preference to "swim", because it is less abstract - especially in past tense.
Sorry, where do you see past tense here?
In any case, you swim a lot if you cover a significant distance in the pool every week. You go swimming a lot if you head to the pool every day, even if all you do there is just splash for a bit and get out.