"How many kilometers will you run today?"
When 何 is used together with a counter (and キロメートル is a counter) it "questions the amount of the measure".
So 何キロメートル is how many kilometres
何歳 is how old
何枚 is how many flat objects
And so on
いくつ is a word used instead of putting 何 before the counter つ (which kilometers are not counted with)
In the duolingo hq one person should go through all the Japanese course and make it coherent: it is illogical that in one set kilometers should be only キロ and in the next one only キロメトル. It's a known fact that there are many ways in which Japanese is written and that perfect orthography is mastered only by few people (mostly in the book business) but it is not an impossible task, expecially if one reads all the reports by the users.
That is true. But there is no person in the Duolingo development team that is responsible for the Japanese course (in fact, I don't know if any of them speak Japanese.) The course, and all the content, was built by volunteers, and all the current moderators, are volunteers. It is getting better, a bit at a time. If you think that there is an issue, report it in the lesson when you find one of the problematic sentences. The moderators see the reports from the lessons, they do not see the comments left here.
I think the wa on this one is perfectly fine because it emphasizes the "today" part. If you're asking this question to someone, you know they run regularly. Since you know this, you're asking them specifically how many kilometers will you run TODAY. You're not asking how many kilometers will you run tomorrow or next week.