"I don't sleep because of the children."
Translation:אני לא ישן בגלל הילדים.
It's just a different emphasis, like if in English you were to say: "Because of the children, I don't sleep". It makes more sense in Duolingo to not rearrange the sentences too much, since you're more likely to get it wrong even though you obviously know the right translation.
That conjunction, בעקבות, can mean "as a result of," but it also can mean "in the footsteps of," as it combines the prep with עקב, "footstep," in the pl. It's a lot to ask the DL computer to accept it in place of בגלל, esp. when this exercise has introduced בגלל but not בעקבות.
You're toying with DL. You've changed the negative sentence positive. The sense of למרות, "despite," would give the sentence a different meaning (esp. if you retain the negative) and the other meanings of למרות, such as "though" and "even though," do not make sense with or without לא.
If the reason is a complete sentence in itself, you add ש. If it's just a noun phrase, you don't. אני לא ישן בגלל שהילדים צועקים. In English there's the same distinction - "because" vs. "because of", except it's reversed - the extra word is needed for a noun phrase, and omitted for a complete sentence.