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)"
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