A good way to differentiate simple from continuous is that simple describes how something is, as in characteristics, while continuous describes an isolated occurrence - Edward Calver, Language, Vol 22 gives a good account of this concept.
"Cats climb trees" - present simple, describes a cat's characteristic.
"The cat is climbing a tree" - present continuous, describes a single occurrence of a cat running up a tree.
"David walks to work" - present simple, describing a characteristic of David.
"David is walking to work" - present continuous, describing a single occurrence of David commuting on foot.
Using that, and looking at the second sentence in your question, it mentions "...at least five days a week". That is not a single occurrence, and hence cannot be continuous. That rules out b (is he exercising - is swimming) and d (does he exercise - is swimming).
Looking at the first sentence, that is asking "how often...", and the question is about exercising which is something the anonymous he does, and as it is a characteristic rather than one occurrence, should be simple.
The only answer that fits is a (does he exercise - swims)
Answer c) - "how often is he exercising" - is conceivable, but so non-standard that searching BNC, COCA, and Google Books gets no hits. Even a straight Google search gets only two hits.