This is really a question about English, not Dutch. One can argue about whether your sentence is correct. This is clearly about a habit, so simple present is required unless we are thinking about short-term changes in the habit. Obviously in a habit that is measured by times per month, short-term can only mean over at least a couple of months. Example: "You told me you swim twice per month, but we've met here at the pool twenty times in July and August alone. How many times per month are you swimming now?" It's hard to come up with an example that doesn't have some additional temporal specification in our sentence, though.
In Dutch, words that occur primarily after numbers typically don't get the plural if the entire phrase (such as "vijf keer" or "vijf meter") can be considered a unit of measurement. They only get the plural if we are looking at the individual units rather than the entire measurement, as in: "Each of the last five times he was late."
Good to know. Fortunately it's easy to remember if you think of the obvious reason for these irregularities concerning third person -t. The -t was once always there, but the people started pronouncing it weaker and weaker - except when the verb is stressed (as in jij/u zwemt) or when a vowel follows immediately so that the t is pronounced as if it started the next syllable (as in zwemt u but not in zwem je).
In languages with a less regular orthography such as e.g. German and French, there are similar phenomena in pronunciation, but they rarely make it into the spelling.
I didn't think of it so much in the sense of number, rather it was the first translation that came to my head. If it doesn't mean, or at least have a meaning that can be made to represent "how much time do you swim per month?", then how would you word it in Dutch instead? Also, I found other examples with similar constructions that could still be understandable whether you wanted to ask "how much time do you -blank- per -blank-" versus "how many times do you -blank- per -blank-". However, I'll admit, I don't even know if "how much time do you (etc.)" is even a proper construction in English, it's just something I've heard/used often. Googling it now. :)
You just have to learn that keer is times in the sense of repetitions, and tijd is time as the dimension / the thing that passes. Dutch has completely separate words for these completely separate senses; in English it's more or less a single word for both senses.
how many times = hoeveel keer.
how much time = hoeveel tijd.
I think the latter construction is equally bad style in both languages.
I did find a source that suggested the word "often", and I believe that would be a more appropriate choice. http://learnenglish.britishcouncil.org/en/english-grammar/adverbials/adverbials-time/how-often Notice they don't mention anything about "how much time" or "how many times". "How often do you (etc.)" seems to be considered the most proper construction, and to me it's easy to see why. I appreciate your input though, it helped me a bit.