As one of the translations given for задача is challenge why is it not possible to say "It is the most difficult challenge"?
это stands in for "this is" or "it is". Basically "this [unspecified thing] is the hardest problem."
If you used эта, it would be "This hardest problem", a sentence fragment. This hardest problem is what?
You could rearrange the sentence though: эта задача самая трудная (this problem is the hardest (one)"
I wrote "This problem is the hardest" and it was marked incorrect. Is it simply a matter of word order?
Would this only be used in the sense of a problem on a test or also for a social problem such as homelessness?
Not always. It's often superlative. It can also be used in a couple other ways. Wiktionary is a good resource as well. It also explains the definitive pronoun use. https://en.m.wiktionary.org/wiki/%D1%81%D0%B0%D0%BC%D1%8B%D0%B9